diff --git a/src/scimlfunctions.jl b/src/scimlfunctions.jl
index e783c5277..c62e8d838 100644
--- a/src/scimlfunctions.jl
+++ b/src/scimlfunctions.jl
@@ -455,6 +455,7 @@ SplitFunction{iip,specialize}(f1,f2;
                              jvp = __has_jvp(f1) ? f1.jvp : nothing,
                              vjp = __has_vjp(f1) ? f1.vjp : nothing,
                              jac_prototype = __has_jac_prototype(f1) ? f1.jac_prototype : nothing,
+                             W_prototype = __has_W_prototype(f1) ? f1.W_prototype : nothing,
                              sparsity = __has_sparsity(f1) ? f1.sparsity : jac_prototype,
                              paramjac = __has_paramjac(f1) ? f1.paramjac : nothing,
                              colorvec = __has_colorvec(f1) ? f1.colorvec : nothing,
@@ -484,6 +485,11 @@ the usage of the `SplitFunction`. These include:
   as the prototype and integrators will specialize on this structure where possible. Non-structured
   sparsity patterns should use a `SparseMatrixCSC` with a correct sparsity pattern for the Jacobian.
   The default is `nothing`, which means a dense Jacobian.
+- `W_prototype`: a prototype matrix matching the type that matches the W matrix. For example,
+  if the Jacobian is tridiagonal, and the mass_matrix is diagonal, then an appropriately sized `Tridiagonal`
+  matrix can be used as the prototype and integrators will specialize on this structure where possible. Non-structured
+  sparsity patterns should use a `SparseMatrixCSC` with a correct sparsity pattern for the W matrix.
+  The default is `nothing`, which means a W of appropriate type for the jacobian and linear solver
 - `paramjac(pJ,u,p,t)`: returns the parameter Jacobian ``\frac{df_1}{dp}``.
 - `colorvec`: a color vector according to the SparseDiffTools.jl definition for the sparsity
   pattern of the `jac_prototype`. This specializes the Jacobian construction when using
@@ -3080,7 +3086,7 @@ SDEFunction(f::SDEFunction; kwargs...) = f
 
 @add_kwonly function SplitSDEFunction(f1, f2, g, mass_matrix, cache, analytic, tgrad, jac,
         jvp, vjp,
-        jac_prototype, Wfact, Wfact_t, paramjac, observed,
+        jac_prototype, W_prototype, Wfact, Wfact_t, paramjac, observed,
         colorvec, sys)
     f1 = f1 isa AbstractSciMLOperator ? f1 : SDEFunction(f1)
     f2 = SDEFunction(f2)
@@ -3091,7 +3097,7 @@ SDEFunction(f::SDEFunction; kwargs...) = f
         typeof(Wfact), typeof(Wfact_t), typeof(paramjac), typeof(observed),
         typeof(colorvec),
         typeof(sys)}(f1, f2, mass_matrix, cache, analytic, tgrad, jac,
-        jac_prototype, Wfact, Wfact_t, paramjac, observed, colorvec, sys)
+        jac_prototype, W_prototype, Wfact, Wfact_t, paramjac, observed, colorvec, sys)
 end
 
 function SplitSDEFunction{iip, specialize}(f1, f2, g;