diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index f8bec27c..f62da45b 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -17,7 +17,7 @@ jobs:
       fail-fast: false
       matrix:
         include:
-          - version: '1.6'
+          - version: 'lts'
             os: ubuntu-latest
             arch: x64
           - version: '1'
diff --git a/src/NonLinearProgram/NonLinearProgram.jl b/src/NonLinearProgram/NonLinearProgram.jl
index c31eb2e7..559309fd 100644
--- a/src/NonLinearProgram/NonLinearProgram.jl
+++ b/src/NonLinearProgram/NonLinearProgram.jl
@@ -552,8 +552,11 @@ function DiffOpt.reverse_differentiate!(model::Model; tol = 1e-6)
         # Compute Jacobian
         Δs, df_dp = _compute_sensitivity(model; tol = tol)
         Δp = if !iszero(model.input_cache.dobj)
-            model.input_cache.dobj * df_dp
+            df_dp'model.input_cache.dobj
         else
+            zeros(length(cache.params))
+        end
+        begin
             num_primal = length(cache.primal_vars)
             # Fetch primal sensitivities
             Δx = zeros(num_primal)
@@ -589,7 +592,7 @@ function DiffOpt.reverse_differentiate!(model::Model; tol = 1e-6)
             Δw = zeros(size(Δs, 1))
             Δw[1:num_primal] = Δx
             Δw[cache.index_duals] = Δdual
-            Δp = Δs' * Δw
+            Δp += Δs' * Δw
         end
 
         Δp_dict = Dict{MOI.ConstraintIndex,Float64}(
diff --git a/src/diff_opt.jl b/src/diff_opt.jl
index 83f9063d..065fc4a8 100644
--- a/src/diff_opt.jl
+++ b/src/diff_opt.jl
@@ -31,6 +31,7 @@ Base.@kwdef mutable struct InputCache
         MOIDD.DoubleDict{MOI.VectorAffineFunction{Float64}}() # also includes G for QPs
     objective::Union{Nothing,MOI.AbstractScalarFunction} = nothing
     factorization::Union{Nothing,Function} = nothing
+    allow_objective_and_solution_input::Bool = false
 end
 
 function Base.empty!(cache::InputCache)
@@ -122,6 +123,8 @@ MOI.set(model, DiffOpt.NonLinearKKTJacobianFactorization(), factorization)
 """
 struct NonLinearKKTJacobianFactorization <: MOI.AbstractModelAttribute end
 
+struct AllowObjectiveAndSolutionInput <: MOI.AbstractModelAttribute end
+
 """
     ForwardConstraintFunction <: MOI.AbstractConstraintAttribute
 
@@ -440,6 +443,15 @@ function MOI.set(
     return
 end
 
+function MOI.set(
+    model::AbstractModel,
+    ::AllowObjectiveAndSolutionInput,
+    allow::Bool,
+)
+    model.input_cache.allow_objective_and_solution_input = allow
+    return
+end
+
 function MOI.set(
     model::AbstractModel,
     ::ReverseVariablePrimal,
diff --git a/src/jump_moi_overloads.jl b/src/jump_moi_overloads.jl
index f402ac35..6251215a 100644
--- a/src/jump_moi_overloads.jl
+++ b/src/jump_moi_overloads.jl
@@ -29,6 +29,14 @@ function MOI.set(
     return MOI.set(JuMP.backend(model), attr, factorization)
 end
 
+function MOI.set(
+    model::JuMP.Model,
+    attr::AllowObjectiveAndSolutionInput,
+    allow::Bool,
+)
+    return MOI.set(JuMP.backend(model), attr, allow)
+end
+
 function MOI.set(
     model::JuMP.Model,
     attr::ForwardObjectiveFunction,
diff --git a/src/moi_wrapper.jl b/src/moi_wrapper.jl
index 1617834d..cfc4cf07 100644
--- a/src/moi_wrapper.jl
+++ b/src/moi_wrapper.jl
@@ -557,9 +557,10 @@ function reverse_differentiate!(model::Optimizer)
     end
     if !iszero(model.input_cache.dobj) &&
        (!isempty(model.input_cache.dx) || !isempty(model.input_cache.dy))
-        error(
-            "Cannot compute the reverse differentiation with both solution sensitivities and objective sensitivities.",
-        )
+        if !MOI.get(model, AllowObjectiveAndSolutionInput())
+            @warn "Computing reverse differentiation with both solution sensitivities and objective sensitivities. " *
+                  "Set `DiffOpt.AllowObjectiveAndSolutionInput()` to `true` to silence this warning."
+        end
     end
     diff = _diff(model)
     MOI.set(
@@ -567,6 +568,11 @@ function reverse_differentiate!(model::Optimizer)
         NonLinearKKTJacobianFactorization(),
         model.input_cache.factorization,
     )
+    MOI.set(
+        diff,
+        AllowObjectiveAndSolutionInput(),
+        model.input_cache.allow_objective_and_solution_input,
+    )
     for (vi, value) in model.input_cache.dx
         MOI.set(diff, ReverseVariablePrimal(), model.index_map[vi], value)
     end
@@ -604,6 +610,11 @@ function forward_differentiate!(model::Optimizer)
         NonLinearKKTJacobianFactorization(),
         model.input_cache.factorization,
     )
+    MOI.set(
+        diff,
+        AllowObjectiveAndSolutionInput(),
+        model.input_cache.allow_objective_and_solution_input,
+    )
     T = Float64
     list = MOI.get(
         model,
@@ -1033,6 +1044,10 @@ function MOI.supports(
     return true
 end
 
+function MOI.supports(::Optimizer, ::AllowObjectiveAndSolutionInput, ::Bool)
+    return true
+end
+
 function MOI.set(
     model::Optimizer,
     ::NonLinearKKTJacobianFactorization,
@@ -1042,10 +1057,19 @@ function MOI.set(
     return
 end
 
+function MOI.set(model::Optimizer, ::AllowObjectiveAndSolutionInput, allow)
+    model.input_cache.allow_objective_and_solution_input = allow
+    return
+end
+
 function MOI.get(model::Optimizer, ::NonLinearKKTJacobianFactorization)
     return model.input_cache.factorization
 end
 
+function MOI.get(model::Optimizer, ::AllowObjectiveAndSolutionInput)
+    return model.input_cache.allow_objective_and_solution_input
+end
+
 function MOI.set(model::Optimizer, attr::MOI.AbstractOptimizerAttribute, value)
     return MOI.set(model.optimizer, attr, value)
 end
diff --git a/test/nlp_program.jl b/test/nlp_program.jl
index c266c715..a3adf3d6 100644
--- a/test/nlp_program.jl
+++ b/test/nlp_program.jl
@@ -644,14 +644,15 @@ function test_ObjectiveSensitivity_model1()
     set_silent(model)
 
     # Parameters
-    @variable(model, p ∈ MOI.Parameter(1.5))
+    p_val = 1.5
+    @variable(model, p ∈ MOI.Parameter(p_val))
 
     # Variables
     @variable(model, x)
 
     # Constraints
     @constraint(model, x * sin(p) == 1)
-    @objective(model, Min, sum(x))
+    @objective(model, Min, 2 * x)
 
     optimize!(model)
     @assert is_solved_and_feasible(model)
@@ -665,19 +666,42 @@ function test_ObjectiveSensitivity_model1()
 
     # Test Objective Sensitivity wrt parameters
     df_dp = MOI.get(model, DiffOpt.ForwardObjectiveSensitivity())
-    @test isapprox(df_dp, -0.0071092; atol = 1e-4)
+    df = -2cos(p_val) / sin(p_val)^2
+    @test isapprox(df_dp, df * Δp; atol = 1e-4)
 
     # Clean up
     DiffOpt.empty_input_sensitivities!(model)
 
-    # Set Too Many Sensitivities
+    # Test both obj and solution inputs
     Δf = 0.5
     MOI.set(model, DiffOpt.ReverseObjectiveSensitivity(), Δf)
+    MOI.set(model, DiffOpt.ReverseVariablePrimal(), x, Δp)
 
-    MOI.set(model, DiffOpt.ReverseVariablePrimal(), x, 1.0)
+    msg = "Computing reverse differentiation with both solution sensitivities and objective sensitivities. Set `DiffOpt.AllowObjectiveAndSolutionInput()` to `true` to silence this warning."
+    @test_logs (:warn, msg) DiffOpt.reverse_differentiate!(model)
+    MOI.set(model, DiffOpt.AllowObjectiveAndSolutionInput(), true)
+    @test_nowarn DiffOpt.reverse_differentiate!(model)
 
-    # Compute derivatives
-    @test_throws ErrorException DiffOpt.reverse_differentiate!(model)
+    dp_combined =
+        MOI.get(model, DiffOpt.ReverseConstraintSet(), ParameterRef(p)).value
+
+    ε = 1e-6
+    df_dp_fdpos = begin
+        set_parameter_value(p, p_val + ε)
+        optimize!(model)
+        Δf * objective_value(model) + Δp * value(x)
+    end
+    df_dp_fdneg = begin
+        set_parameter_value(p, p_val - ε)
+        optimize!(model)
+        Δf * objective_value(model) + Δp * value(x)
+    end
+    df_dp_fd = (df_dp_fdpos - df_dp_fdneg) / (2ε)
+
+    @test isapprox(df_dp_fd, dp_combined)
+
+    set_parameter_value(p, p_val)
+    optimize!(model)
 
     DiffOpt.empty_input_sensitivities!(model)
 
@@ -691,7 +715,7 @@ function test_ObjectiveSensitivity_model1()
     # Test Objective Sensitivity wrt parameters
     dp = MOI.get(model, DiffOpt.ReverseConstraintSet(), ParameterRef(p)).value
 
-    @test isapprox(dp, -0.0355464; atol = 1e-4)
+    @test isapprox(dp, df * Δf; atol = 1e-4)
 end
 
 function test_ObjectiveSensitivity_model2()