diff --git a/src/Bridges/Constraint/bridges/vectorize.jl b/src/Bridges/Constraint/bridges/vectorize.jl
index cbf572759a..9f60285e28 100644
--- a/src/Bridges/Constraint/bridges/vectorize.jl
+++ b/src/Bridges/Constraint/bridges/vectorize.jl
@@ -64,6 +64,14 @@ function MOI.supports_constraint(
     return true
 end
 
+function MOI.supports_constraint(
+    ::Type{VectorizeBridge{T}},
+    ::Type{MOI.ScalarNonlinearFunction},
+    ::Type{<:MOI.Utilities.ScalarLinearSet{T}},
+) where {T}
+    return false
+end
+
 function MOI.Bridges.added_constrained_variable_types(::Type{<:VectorizeBridge})
     return Tuple{Type}[]
 end
diff --git a/src/Utilities/functions.jl b/src/Utilities/functions.jl
index 4946acdf67..6c2b92d4d5 100644
--- a/src/Utilities/functions.jl
+++ b/src/Utilities/functions.jl
@@ -1817,28 +1817,56 @@ end
 ### ScalarNonlinearFunction
 
 function promote_operation(
-    ::typeof(-),
-    ::Type{T},
+    ::Union{typeof(+),typeof(-)},
+    ::Type{<:Number},
     ::Type{MOI.ScalarNonlinearFunction},
+)
+    return MOI.ScalarNonlinearFunction
+end
+
+function operate(
+    ::typeof(-),
     ::Type{T},
+    f::MOI.ScalarNonlinearFunction,
 ) where {T}
-    return MOI.ScalarNonlinearFunction
+    if f.head == :- && length(f.args) == 1
+        # A simplification for -(-(f)) into f, but only if f is an SNF.
+        if f.args[1] isa MOI.ScalarNonlinearFunction
+            return f.args[1]
+        end
+    end
+    return MOI.ScalarNonlinearFunction(:-, Any[f])
 end
 
 function promote_operation(
-    ::typeof(-),
+    ::Union{typeof(+),typeof(-),typeof(*),typeof(/)},
     ::Type{T},
     ::Type{MOI.ScalarNonlinearFunction},
-    ::Type{MOI.VariableIndex},
-) where {T}
+    ::Type{S},
+) where {
+    T<:Number,
+    S<:Union{
+        T,
+        MOI.VariableIndex,
+        MOI.ScalarAffineFunction{T},
+        MOI.ScalarQuadraticFunction{T},
+        MOI.ScalarNonlinearFunction,
+    },
+}
     return MOI.ScalarNonlinearFunction
 end
 
 function operate(
-    op::Union{typeof(+),typeof(-)},
+    op::Union{typeof(+),typeof(-),typeof(*),typeof(/)},
     ::Type{T},
     f::MOI.ScalarNonlinearFunction,
-    g::ScalarQuadraticLike{T},
+    g::Union{
+        T,
+        MOI.VariableIndex,
+        MOI.ScalarAffineFunction{T},
+        MOI.ScalarQuadraticFunction{T},
+        MOI.ScalarNonlinearFunction,
+    },
 ) where {T}
     return MOI.ScalarNonlinearFunction(Symbol(op), Any[f, g])
 end
diff --git a/test/Bridges/Constraint/flip_sign.jl b/test/Bridges/Constraint/flip_sign.jl
index 167c594f1f..9aaaa18cf2 100644
--- a/test/Bridges/Constraint/flip_sign.jl
+++ b/test/Bridges/Constraint/flip_sign.jl
@@ -337,6 +337,17 @@ function test_runtests()
         -1.5 * x <= -1.0
         """,
     )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.GreaterToLessBridge,
+        """
+        variables: x
+        ScalarNonlinearFunction(1.5 * x) >= 1.0
+        """,
+        """
+        variables: x
+        ScalarNonlinearFunction(-(1.5 * x)) <= -1.0
+        """,
+    )
     MOI.Bridges.runtests(
         MOI.Bridges.Constraint.LessToGreaterBridge,
         """
@@ -359,6 +370,17 @@ function test_runtests()
         -1.5 * x >= -1.0
         """,
     )
+    MOI.Bridges.runtests(
+        MOI.Bridges.Constraint.LessToGreaterBridge,
+        """
+        variables: x
+        ScalarNonlinearFunction(1.5 * x) <= 1.0
+        """,
+        """
+        variables: x
+        ScalarNonlinearFunction(-(1.5 * x)) >= -1.0
+        """,
+    )
     MOI.Bridges.runtests(
         MOI.Bridges.Constraint.NonnegToNonposBridge,
         """
diff --git a/test/Bridges/Constraint/vectorize.jl b/test/Bridges/Constraint/vectorize.jl
index 79c17546d9..e51e6cb398 100644
--- a/test/Bridges/Constraint/vectorize.jl
+++ b/test/Bridges/Constraint/vectorize.jl
@@ -238,6 +238,28 @@ function test_runtests()
     return
 end
 
+MOI.Utilities.@model(
+    Model2179,
+    (),
+    (MOI.GreaterThan, MOI.LessThan),
+    (),
+    (),
+    (),
+    (MOI.ScalarAffineFunction,),
+    (),
+    ()
+)
+
+function test_unsupported_ScalarNonlinearFunction()
+    model = MOI.instantiate(Model2179{Float64}; with_bridge_type = Float64)
+    MOI.supports_constraint(
+        model,
+        MOI.ScalarNonlinearFunction,
+        MOI.GreaterThan{Float64},
+    )
+    return
+end
+
 end  # module
 
 TestConstraintVectorize.runtests()