diff --git a/src/QCQP/MOI_wrapper.jl b/src/QCQP/MOI_wrapper.jl
index d64e37f..6597fa9 100644
--- a/src/QCQP/MOI_wrapper.jl
+++ b/src/QCQP/MOI_wrapper.jl
@@ -10,9 +10,16 @@ mutable struct Optimizer{T,O<:MOI.ModelLike} <: MOI.AbstractOptimizer
     index_map::Dict{MOI.ConstraintIndex,MOI.ConstraintIndex}
 end
 
-function Optimizer{T}(model::MOI.ModelLike) where {T}
-    return Optimizer{T,typeof(model)}(
-        model,
+function Optimizer{T}(optimizer::MOI.ModelLike) where {T}
+    if !MOI.supports_incremental_interface(optimizer)
+        cache = MOI.default_cache(optimizer, T)
+        optimizer = MOI.Utilities.CachingOptimizer(cache, optimizer)
+    end
+    # This bridge layer is needed for instance if `optimizer` needs to bridge
+    # quadratic objective into quadratic constraints with a slack bridge (e.g., like SCIP)
+    inner = MOI.Bridges.full_bridge_optimizer(optimizer, T)
+    return Optimizer{T,typeof(inner)}(
+        inner,
         nothing,
         DataStructures.OrderedDict{Type,MOI.Utilities.VectorOfConstraints}(),
         Dict{MOI.ConstraintIndex,MOI.ConstraintIndex}(),
diff --git a/test/qcqp.jl b/test/qcqp.jl
index d08d3fb..7bb1183 100644
--- a/test/qcqp.jl
+++ b/test/qcqp.jl
@@ -49,6 +49,25 @@ MOI.Utilities.@model(
     (),
 )
 
+MOI.Utilities.@model(
+    AffineObjectiveModel,
+    (),
+    (MOI.LessThan, MOI.GreaterThan, MOI.EqualTo, MOI.Interval),
+    (),
+    (),
+    (),
+    (MOI.ScalarAffineFunction, MOI.ScalarQuadraticFunction),
+    (),
+    (),
+)
+
+function MOI.supports(
+    ::AffineObjectiveModel{T},
+    ::MOI.ObjectiveFunction{F},
+) where {T,F<:MOI.AbstractFunction}
+    return F == MOI.ScalarAffineFunction{T}
+end
+
 function MOI.supports(
     ::Model,
     ::MOI.ObjectiveFunction{MOI.ScalarNonlinearFunction},
@@ -336,6 +355,21 @@ function test_start(x, y, T)
     @test sort(MOI.get(inner, MOI.VariablePrimalStart(), vis)) == T[2, 3, 4, 9]
 end
 
+function test_inner_bridge(x, y, T)
+    # The quadratic objective should be bridged after the QCQP layer
+    inner = AffineObjectiveModel{T}()
+    model = PolyJuMP.QCQP.Optimizer{T}(inner)
+    a = MOI.add_variable(model)
+    b = MOI.add_variable(model)
+    p = PolyJuMP.ScalarPolynomialFunction(one(T) * x^3 - x * y^2, [a, b])
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+    MOI.set(model, MOI.ObjectiveFunction{typeof(p)}(), p)
+    MOI.Utilities.final_touch(model, nothing)
+    F = MOI.ScalarAffineFunction{T}
+    @test MOI.ObjectiveFunction{F}() in
+          MOI.get(inner, MOI.ListOfModelAttributesSet())
+end
+
 function runtests(x, y)
     for name in names(@__MODULE__; all = true)
         if startswith("$name", "test_")