diff --git a/src/structural_transformation/StructuralTransformations.jl b/src/structural_transformation/StructuralTransformations.jl
index 681025cb81..1cd4c7615f 100644
--- a/src/structural_transformation/StructuralTransformations.jl
+++ b/src/structural_transformation/StructuralTransformations.jl
@@ -59,7 +59,7 @@ using DocStringExtensions
 export tearing, dae_index_lowering, check_consistency
 export dummy_derivative
 export sorted_incidence_matrix,
-       pantelides!, pantelides_reassemble, tearing_reassemble, find_solvables!,
+       pantelides!, pantelides_reassemble, find_solvables!,
        linear_subsys_adjmat!
 export tearing_substitution
 export torn_system_jacobian_sparsity
@@ -69,9 +69,9 @@ export computed_highest_diff_variables
 export shift2term, lower_shift_varname, simplify_shifts, distribute_shift
 
 include("utils.jl")
+include("tearing.jl")
 include("pantelides.jl")
 include("bipartite_tearing/modia_tearing.jl")
-include("tearing.jl")
 include("symbolics_tearing.jl")
 include("partial_state_selection.jl")
 include("codegen.jl")
diff --git a/src/structural_transformation/bipartite_tearing/modia_tearing.jl b/src/structural_transformation/bipartite_tearing/modia_tearing.jl
index 5da873afdf..b931c61137 100644
--- a/src/structural_transformation/bipartite_tearing/modia_tearing.jl
+++ b/src/structural_transformation/bipartite_tearing/modia_tearing.jl
@@ -62,19 +62,22 @@ function tear_graph_block_modia!(var_eq_matching, ict, solvable_graph, eqs, vars
     return nothing
 end
 
-function build_var_eq_matching(structure::SystemStructure, ::Type{U} = Unassigned;
-        varfilter::F2 = v -> true, eqfilter::F3 = eq -> true) where {U, F2, F3}
+function build_var_eq_matching(structure::SystemStructure;
+        varfilter::F2, eqfilter::F3) where {F2, F3}
     @unpack graph, solvable_graph = structure
-    var_eq_matching = maximal_matching(graph, eqfilter, varfilter, U)
+    var_eq_matching = maximal_matching(graph, eqfilter, varfilter, MatchedVarT)
     matching_len = max(length(var_eq_matching),
         maximum(x -> x isa Int ? x : 0, var_eq_matching, init = 0))
     return complete(var_eq_matching, matching_len), matching_len
 end
 
-function tear_graph_modia(structure::SystemStructure, isder::F = nothing,
-        ::Type{U} = Unassigned;
-        varfilter::F2 = v -> true,
-        eqfilter::F3 = eq -> true) where {F, U, F2, F3}
+@kwdef struct ModiaTearing{F, F2, F3}
+    isder::F = nothing
+    varfilter::F2 = Returns(true)
+    eqfilter::F3 = Returns(true)
+end
+
+function (alg::ModiaTearing)(structure::SystemStructure)
     # It would be possible here to simply iterate over all variables and attempt to
     # use tearEquations! to produce a matching that greedily selects the minimal
     # number of torn variables. However, we can do this process faster if we first
@@ -86,8 +89,11 @@ function tear_graph_modia(structure::SystemStructure, isder::F = nothing,
     # to have optimal solutions that cannot be found by this process. We will not
     # find them here [TODO: It would be good to have an explicit example of this.]
 
+    isder = alg.isder
+    varfilter = alg.varfilter
+    eqfilter = alg.eqfilter
     @unpack graph, solvable_graph = structure
-    var_eq_matching, matching_len = build_var_eq_matching(structure, U; varfilter, eqfilter)
+    var_eq_matching, matching_len = build_var_eq_matching(structure; varfilter, eqfilter)
     full_var_eq_matching = copy(var_eq_matching)
     var_sccs = find_var_sccs(graph, var_eq_matching)
     vargraph = DiCMOBiGraph{true}(graph, 0, Matching(matching_len))
@@ -126,5 +132,6 @@ function tear_graph_modia(structure::SystemStructure, isder::F = nothing,
         tear_graph_block_modia!(var_eq_matching, ict, solvable_graph, free_eqs,
             BitSet(free_vars), isder)
     end
-    return var_eq_matching, full_var_eq_matching, var_sccs
+
+    return TearingResult(var_eq_matching, full_var_eq_matching, var_sccs), (;)
 end
diff --git a/src/structural_transformation/partial_state_selection.jl b/src/structural_transformation/partial_state_selection.jl
index ab8e7f0f3d..98e40e9988 100644
--- a/src/structural_transformation/partial_state_selection.jl
+++ b/src/structural_transformation/partial_state_selection.jl
@@ -1,11 +1,9 @@
-struct SelectedState end
-
 function dummy_derivative_graph!(state::TransformationState, jac = nothing;
         state_priority = nothing, log = Val(false), kwargs...)
     state.structure.solvable_graph === nothing && find_solvables!(state; kwargs...)
     complete!(state.structure)
     var_eq_matching = complete(pantelides!(state; kwargs...))
-    dummy_derivative_graph!(state.structure, var_eq_matching, jac, state_priority, log)
+    dummy_derivative_graph!(state.structure, var_eq_matching, jac, state_priority, log; kwargs...)
 end
 
 struct DummyDerivativeSummary
@@ -15,7 +13,8 @@ end
 
 function dummy_derivative_graph!(
         structure::SystemStructure, var_eq_matching, jac = nothing,
-        state_priority = nothing, ::Val{log} = Val(false)) where {log}
+        state_priority = nothing, ::Val{log} = Val(false);
+        tearing_alg::TearingAlgorithm = DummyDerivativeTearing(), kwargs...) where {log}
     @unpack eq_to_diff, var_to_diff, graph = structure
     diff_to_eq = invview(eq_to_diff)
     diff_to_var = invview(var_to_diff)
@@ -173,8 +172,9 @@ function dummy_derivative_graph!(
         @warn "The number of dummy derivatives ($n_dummys) does not match the number of differentiated equations ($n_diff_eqs)."
     end
 
-    ret = tearing_with_dummy_derivatives(structure, BitSet(dummy_derivatives))
-    (ret..., DummyDerivativeSummary(var_dummy_scc, var_state_priority))
+    tearing_result, extra = tearing_alg(structure, BitSet(dummy_derivatives))
+    extra = (; extra..., ddsummary = DummyDerivativeSummary(var_dummy_scc, var_state_priority))
+    return tearing_result, extra
 end
 
 function is_present(structure, v)::Bool
@@ -201,7 +201,9 @@ function isdiffed((structure, dummy_derivatives), v)::Bool
     diff_to_var[v] !== nothing && is_some_diff(structure, dummy_derivatives, v)
 end
 
-function tearing_with_dummy_derivatives(structure, dummy_derivatives)
+struct DummyDerivativeTearing <: TearingAlgorithm end
+
+function (::DummyDerivativeTearing)(structure::SystemStructure, dummy_derivatives::Union{BitSet, Tuple{}} = ())
     @unpack var_to_diff = structure
     # We can eliminate variables that are not selected (differential
     # variables). Selected unknowns are differentiated variables that are not
@@ -213,18 +215,18 @@ function tearing_with_dummy_derivatives(structure, dummy_derivatives)
             can_eliminate[v] = true
         end
     end
-    var_eq_matching, full_var_eq_matching,
-    var_sccs = tear_graph_modia(structure,
-        Base.Fix1(isdiffed, (structure, dummy_derivatives)),
-        Union{Unassigned, SelectedState};
-        varfilter = Base.Fix1(getindex, can_eliminate))
+    modia_tearing = ModiaTearing(;
+        isder = Base.Fix1(isdiffed, (structure, dummy_derivatives)),
+        varfilter = Base.Fix1(getindex, can_eliminate)
+    )
+    tearing_result, _ = modia_tearing(structure)
 
     for v in 𝑑vertices(structure.graph)
         is_present(structure, v) || continue
         dv = var_to_diff[v]
         (dv === nothing || !is_some_diff(structure, dummy_derivatives, dv)) && continue
-        var_eq_matching[v] = SelectedState()
+        tearing_result.var_eq_matching[v] = SelectedState()
     end
 
-    return var_eq_matching, full_var_eq_matching, var_sccs, can_eliminate
+    return tearing_result, (; can_eliminate)
 end
diff --git a/src/structural_transformation/symbolics_tearing.jl b/src/structural_transformation/symbolics_tearing.jl
index e079ba30b5..540944bb6a 100644
--- a/src/structural_transformation/symbolics_tearing.jl
+++ b/src/structural_transformation/symbolics_tearing.jl
@@ -1047,9 +1047,15 @@ differential variables.
 - `var_sccs`: The topologically sorted strongly connected components of the system
   according to `full_var_eq_matching`.
 """
-function tearing_reassemble(state::TearingState, var_eq_matching::Matching,
-        full_var_eq_matching::Matching, var_sccs::Vector{Vector{Int}}; simplify = false, mm,
-        array_hack = true, fully_determined = true)
+@kwdef struct DefaultReassembleAlgorithm <: ReassembleAlgorithm
+    simplify::Bool = false
+    array_hack::Bool = true
+end
+
+function (alg::DefaultReassembleAlgorithm)(state::TearingState, tearing_result::TearingResult, mm::Union{SparseMatrixCLIL,  Nothing}; fully_determined::Bool = true, kw...)
+    @unpack simplify, array_hack = alg
+    @unpack var_eq_matching, full_var_eq_matching, var_sccs = tearing_result
+
     extra_eqs_vars = get_extra_eqs_vars(
         state, var_eq_matching, full_var_eq_matching, fully_determined)
     neweqs = collect(equations(state))
@@ -1314,25 +1320,25 @@ end
     ndims = ndims(arr)
 end
 
-function tearing(state::TearingState; kwargs...)
+function tearing(state::TearingState; tearing_alg::TearingAlgorithm = DummyDerivativeTearing(),
+                 kwargs...)
     state.structure.solvable_graph === nothing && find_solvables!(state; kwargs...)
     complete!(state.structure)
-    tearing_with_dummy_derivatives(state.structure, ())
+    tearing_alg(state.structure)
 end
 
 """
-    tearing(sys; simplify=false)
+    tearing(sys)
 
 Tear the nonlinear equations in system. When `simplify=true`, we simplify the
 new residual equations after tearing. End users are encouraged to call [`mtkcompile`](@ref)
 instead, which calls this function internally.
 """
 function tearing(sys::AbstractSystem, state = TearingState(sys); mm = nothing,
-        simplify = false, array_hack = true, fully_determined = true, kwargs...)
-    var_eq_matching, full_var_eq_matching, var_sccs, can_eliminate = tearing(state)
-    invalidate_cache!(tearing_reassemble(
-        state, var_eq_matching, full_var_eq_matching, var_sccs; mm,
-        simplify, array_hack, fully_determined))
+        reassemble_alg::ReassembleAlgorithm = DefaultReassembleAlgorithm(),
+        fully_determined = true, kwargs...)
+    tearing_result, extras = tearing(state; kwargs...)
+    invalidate_cache!(reassemble_alg(state, tearing_result, mm; fully_determined))
 end
 
 """
@@ -1341,8 +1347,9 @@ end
 Perform index reduction and use the dummy derivative technique to ensure that
 the system is balanced.
 """
-function dummy_derivative(sys, state = TearingState(sys); simplify = false,
-        mm = nothing, array_hack = true, fully_determined = true, kwargs...)
+function dummy_derivative(sys, state = TearingState(sys);
+        reassemble_alg::ReassembleAlgorithm = DefaultReassembleAlgorithm(),
+        mm = nothing, fully_determined = true, kwargs...)
     jac = let state = state
         (eqs, vars) -> begin
             symeqs = EquationsView(state)[eqs]
@@ -1364,10 +1371,7 @@ function dummy_derivative(sys, state = TearingState(sys); simplify = false,
             p
         end
     end
-    var_eq_matching, full_var_eq_matching, var_sccs,
-    can_eliminate, summary = dummy_derivative_graph!(
-        state, jac; state_priority,
-        kwargs...)
-    tearing_reassemble(state, var_eq_matching, full_var_eq_matching, var_sccs;
-        simplify, mm, array_hack, fully_determined)
+    tearing_result, extras = dummy_derivative_graph!(
+        state, jac; state_priority, kwargs...)
+    reassemble_alg(state, tearing_result, mm; fully_determined)
 end
diff --git a/src/structural_transformation/tearing.jl b/src/structural_transformation/tearing.jl
index 67933ffe0e..77a004a823 100644
--- a/src/structural_transformation/tearing.jl
+++ b/src/structural_transformation/tearing.jl
@@ -83,3 +83,65 @@ function free_equations(graph, vars_scc, var_eq_matching, varfilter::F) where {F
     end
     findall(!, seen_eqs)
 end
+
+struct SelectedState end
+const MatchingT{T} = Matching{T, Vector{Union{T, Int}}}
+const MatchedVarT = Union{Unassigned, SelectedState}
+const VarEqMatchingT = MatchingT{MatchedVarT}
+
+"""
+    $TYPEDEF
+
+A struct containing the results of tearing.
+
+# Fields
+
+$TYPEDFIELDS
+"""
+struct TearingResult
+    """
+    The variable-equation matching. Differential variables are matched to `SelectedState`.
+    The derivative of a differential variable is matched to the corresponding differential
+    equation. Solved variables are matched to the equation they are solved from. Algebraic
+    variables are matched to `unassigned`.
+    """
+    var_eq_matching::VarEqMatchingT
+    """
+    The variable-equation matching prior to tearing. This is the maximal matching used to
+    compute `var_sccs` (see below). For generating the torn system, `var_eq_matching` is
+    the source of truth. This should only be used to identify algebraic equations in each
+    SCC.
+    """
+    full_var_eq_matching::VarEqMatchingT
+    """
+    The partitioning of variables into strongly connected components (SCCs). The SCCs are
+    sorted in dependency order, so each SCC depends on variables in previous SCCs.
+    """
+    var_sccs::Vector{Vector{Int}}
+end
+
+"""
+    $TYPEDEF
+
+Supertype for all tearing algorithms. A tearing algorithm takes as input the
+`SystemStructure` along with any other necessary arguments.
+
+The output of a tearing algorithm must be a `TearingResult` and a `NamedTuple` of
+any additional data computed in the process that may be useful for further processing.
+"""
+abstract type TearingAlgorithm end
+
+"""
+    $TYPEDEF
+
+Supertype for all reassembling algorithms. A reassembling algorithm takes as input the
+`TearingState`, `TearingResult` and integer incidence matrix `mm::SparseMatrixCLIL`. The
+matrix `mm` may be `nothing`. The algorithm must also accept arbitrary keyword arguments.
+The following keyword arguments will always be provided:
+- `fully_determined::Bool`: flag indicating whether the system is fully determined.
+
+The output of a reassembling algorithm must be the torn system.
+
+A reassemble algorithm must also implement `with_fully_determined`
+"""
+abstract type ReassembleAlgorithm end
diff --git a/src/systems/systems.jl b/src/systems/systems.jl
index 49efb3e1d4..9173be44fc 100644
--- a/src/systems/systems.jl
+++ b/src/systems/systems.jl
@@ -31,12 +31,14 @@ function mtkcompile(
         sys::AbstractSystem; additional_passes = [], simplify = false, split = true,
         allow_symbolic = false, allow_parameter = true, conservative = false, fully_determined = true,
         inputs = Any[], outputs = Any[],
-        disturbance_inputs = Any[],
+        disturbance_inputs = Any[], array_hack = true,
         kwargs...)
     isscheduled(sys) && throw(RepeatedStructuralSimplificationError())
-    newsys′ = __mtkcompile(sys; simplify,
+    reassemble_alg = get(kwargs, :reassemble_alg,
+        StructuralTransformations.DefaultReassembleAlgorithm(; simplify, array_hack))
+    newsys′ = __mtkcompile(sys;
         allow_symbolic, allow_parameter, conservative, fully_determined,
-        inputs, outputs, disturbance_inputs, additional_passes,
+        inputs, outputs, disturbance_inputs, additional_passes, reassemble_alg,
         kwargs...)
     if newsys′ isa Tuple
         @assert length(newsys′) == 2
@@ -59,7 +61,7 @@ function mtkcompile(
     end
 end
 
-function __mtkcompile(sys::AbstractSystem; simplify = false,
+function __mtkcompile(sys::AbstractSystem;
         inputs = Any[], outputs = Any[],
         disturbance_inputs = Any[],
         sort_eqs = true,
@@ -72,7 +74,7 @@ function __mtkcompile(sys::AbstractSystem; simplify = false,
         return sys
     end
     if isempty(equations(sys)) && !is_time_dependent(sys) && !_iszero(cost(sys))
-        return simplify_optimization_system(sys; kwargs..., sort_eqs, simplify)
+        return simplify_optimization_system(sys; kwargs..., sort_eqs)
     end
 
     sys, statemachines = extract_top_level_statemachines(sys)
@@ -94,7 +96,7 @@ function __mtkcompile(sys::AbstractSystem; simplify = false,
     end
     if isempty(brown_vars)
         return mtkcompile!(
-            state; simplify, inputs, outputs, disturbance_inputs, kwargs...)
+            state; inputs, outputs, disturbance_inputs, kwargs...)
     else
         Is = Int[]
         Js = Int[]
@@ -129,7 +131,7 @@ function __mtkcompile(sys::AbstractSystem; simplify = false,
                               if !iszero(new_idxs[i]) &&
                                  invview(var_to_diff)[i] === nothing]
         ode_sys = mtkcompile(
-            sys; simplify, inputs, outputs, disturbance_inputs, kwargs...)
+            sys; inputs, outputs, disturbance_inputs, kwargs...)
         eqs = equations(ode_sys)
         sorted_g_rows = zeros(Num, length(eqs), size(g, 2))
         for (i, eq) in enumerate(eqs)
diff --git a/src/systems/systemstructure.jl b/src/systems/systemstructure.jl
index c867306c34..d05fc74dd0 100644
--- a/src/systems/systemstructure.jl
+++ b/src/systems/systemstructure.jl
@@ -920,13 +920,13 @@ function make_eqs_zero_equals!(ts::TearingState)
     copyto!(get_eqs(ts.sys), neweqs)
 end
 
-function mtkcompile!(state::TearingState; simplify = false,
+function mtkcompile!(state::TearingState;
         check_consistency = true, fully_determined = true, warn_initialize_determined = true,
         inputs = Any[], outputs = Any[],
         disturbance_inputs = Any[],
         kwargs...)
     if !is_time_dependent(state.sys)
-        return _mtkcompile!(state; simplify, check_consistency,
+        return _mtkcompile!(state; check_consistency,
             inputs, outputs, disturbance_inputs,
             fully_determined, kwargs...)
     end
@@ -956,7 +956,7 @@ function mtkcompile!(state::TearingState; simplify = false,
     if length(tss) > 1
         make_eqs_zero_equals!(tss[continuous_id])
         # simplify as normal
-        sys = _mtkcompile!(tss[continuous_id]; simplify,
+        sys = _mtkcompile!(tss[continuous_id];
             inputs = [inputs; clocked_inputs[continuous_id]], outputs, disturbance_inputs,
             check_consistency, fully_determined,
             kwargs...)
@@ -986,13 +986,13 @@ function mtkcompile!(state::TearingState; simplify = false,
         state.sys = sys
     end
 
-    sys = _mtkcompile!(state; simplify, check_consistency,
+    sys = _mtkcompile!(state; check_consistency,
         inputs, outputs, disturbance_inputs,
         fully_determined, kwargs...)
     return sys
 end
 
-function _mtkcompile!(state::TearingState; simplify = false,
+function _mtkcompile!(state::TearingState;
         check_consistency = true, fully_determined = true, warn_initialize_determined = false,
         dummy_derivative = true,
         inputs = Any[], outputs = Any[],
@@ -1014,17 +1014,17 @@ function _mtkcompile!(state::TearingState; simplify = false,
     end
     if fully_determined && dummy_derivative
         sys = ModelingToolkit.dummy_derivative(
-            sys, state; simplify, mm, check_consistency, kwargs...)
+            sys, state; mm, check_consistency, kwargs...)
     elseif fully_determined
         var_eq_matching = pantelides!(state; finalize = false, kwargs...)
         sys = pantelides_reassemble(state, var_eq_matching)
         state = TearingState(sys)
         sys, mm = ModelingToolkit.alias_elimination!(state; fully_determined, kwargs...)
         sys = ModelingToolkit.dummy_derivative(
-            sys, state; simplify, mm, check_consistency, fully_determined, kwargs...)
+            sys, state; mm, check_consistency, fully_determined, kwargs...)
     else
         sys = ModelingToolkit.tearing(
-            sys, state; simplify, mm, check_consistency, fully_determined, kwargs...)
+            sys, state; mm, check_consistency, fully_determined, kwargs...)
     end
     fullunknowns = [observables(sys); unknowns(sys)]
     @set! sys.observed = ModelingToolkit.topsort_equations(observed(sys), fullunknowns)
diff --git a/test/structural_transformation/tearing.jl b/test/structural_transformation/tearing.jl
index 4025f7a298..d6e76918cb 100644
--- a/test/structural_transformation/tearing.jl
+++ b/test/structural_transformation/tearing.jl
@@ -97,8 +97,8 @@ newsys = tearing(sys)
 # e5 [  1           1 |  1 ]
 
 let state = TearingState(sys)
-    torn_matching, = tearing(state)
-    S = StructuralTransformations.reordered_matrix(sys, torn_matching)
+    result, = tearing(state)
+    S = StructuralTransformations.reordered_matrix(sys, result.var_eq_matching)
     @test S == [1 0 0 0 1
                 1 1 0 0 0
                 1 1 1 0 0