diff --git a/src/Bridges/Constraint/bridges/AbstractToIntervalBridge.jl b/src/Bridges/Constraint/bridges/AbstractToIntervalBridge.jl
index f486d3a697..da3b0e2533 100644
--- a/src/Bridges/Constraint/bridges/AbstractToIntervalBridge.jl
+++ b/src/Bridges/Constraint/bridges/AbstractToIntervalBridge.jl
@@ -38,7 +38,7 @@ end
 function MOI.modify(
     model::MOI.ModelLike,
     bridge::AbstractToIntervalBridge,
-    change::MOI.ScalarCoefficientChange,
+    change::Union{MOI.ScalarConstantChange,MOI.ScalarCoefficientChange},
 )
     MOI.modify(model, bridge.constraint, change)
     return
diff --git a/src/Bridges/Constraint/bridges/FlipSignBridge.jl b/src/Bridges/Constraint/bridges/FlipSignBridge.jl
index 463a11b9f7..bda37b7294 100644
--- a/src/Bridges/Constraint/bridges/FlipSignBridge.jl
+++ b/src/Bridges/Constraint/bridges/FlipSignBridge.jl
@@ -67,6 +67,16 @@ function MOI.modify(
     return
 end
 
+function MOI.modify(
+    model::MOI.ModelLike,
+    bridge::FlipSignBridge,
+    change::MOI.ScalarConstantChange,
+)
+    new_change = MOI.ScalarConstantChange(-change.new_constant)
+    MOI.modify(model, bridge.constraint, new_change)
+    return
+end
+
 function MOI.modify(
     model::MOI.ModelLike,
     bridge::FlipSignBridge,
@@ -83,6 +93,16 @@ function MOI.modify(
     return
 end
 
+function MOI.modify(
+    model::MOI.ModelLike,
+    bridge::FlipSignBridge,
+    change::MOI.VectorConstantChange,
+)
+    new_change = MOI.VectorConstantChange(-change.new_constant)
+    MOI.modify(model, bridge.constraint, new_change)
+    return
+end
+
 """
     GreaterToLessBridge{T,F,G} <: Bridges.Constraint.AbstractBridge
 
diff --git a/src/Bridges/Constraint/bridges/NormSpecialCaseBridge.jl b/src/Bridges/Constraint/bridges/NormSpecialCaseBridge.jl
index de6bc7a0fe..0af8574b2a 100644
--- a/src/Bridges/Constraint/bridges/NormSpecialCaseBridge.jl
+++ b/src/Bridges/Constraint/bridges/NormSpecialCaseBridge.jl
@@ -38,6 +38,15 @@ function concrete_bridge_type(
     return NormSpecialCaseBridge{S,T,F}
 end
 
+function MOI.modify(
+    model::MOI.ModelLike,
+    bridge::NormSpecialCaseBridge,
+    change::Union{MOI.VectorConstantChange,MOI.MultirowChange},
+)
+    MOI.modify(model, bridge.constraint, change)
+    return
+end
+
 """
     NormOneConeToNormConeBridge{T,F} <: Bridges.Constraint.AbstractBridge
 
diff --git a/src/Bridges/Constraint/set_map.jl b/src/Bridges/Constraint/set_map.jl
index fed3e8f0d7..70062db687 100644
--- a/src/Bridges/Constraint/set_map.jl
+++ b/src/Bridges/Constraint/set_map.jl
@@ -226,60 +226,6 @@ function MOI.set(
     return
 end
 
-# By linearity of the map, we can just change the constant/coefficient
-
-function MOI.modify(
-    model::MOI.ModelLike,
-    bridge::BT,
-    change::MOI.ScalarConstantChange,
-) where {BT<:MultiSetMapBridge}
-    new_constant = MOI.Bridges.map_function(BT, change.new_constant)
-    MOI.modify(model, bridge.constraint, MOI.ScalarConstantChange(new_constant))
-    return
-end
-
-function MOI.modify(
-    model::MOI.ModelLike,
-    bridge::BT,
-    change::MOI.VectorConstantChange,
-) where {BT<:MultiSetMapBridge}
-    new_constant = MOI.Bridges.map_function(BT, change.new_constant)
-    MOI.modify(model, bridge.constraint, MOI.VectorConstantChange(new_constant))
-    return
-end
-
-function MOI.modify(
-    model::MOI.ModelLike,
-    bridge::BT,
-    change::MOI.ScalarCoefficientChange,
-) where {BT<:MultiSetMapBridge}
-    new_coefficient = MOI.Bridges.map_function(BT, change.new_coefficient)
-    new_change = MOI.ScalarCoefficientChange(change.variable, new_coefficient)
-    MOI.modify(model, bridge.constraint, new_change)
-    return
-end
-
-function MOI.modify(
-    model::MOI.ModelLike,
-    bridge::BT,
-    change::MOI.MultirowChange{T},
-) where {T,BT<:MultiSetMapBridge{T}}
-    # It is important here that `change.new_coefficients` contains the complete
-    # new sparse column associated to the variable. Calling modify twice with
-    # part of the column won't work since  the linear map might reset all the
-    # column each time.
-    n = MOI.dimension(MOI.get(model, MOI.ConstraintSet(), bridge.constraint))
-    dense = zeros(T, n)
-    for (row, value) in change.new_coefficients
-        dense[row] += value
-    end
-    map_dense = MOI.Bridges.map_function(BT, dense)
-    sparse = Tuple{Int64,T}[rv for rv in enumerate(map_dense) if !iszero(rv[2])]
-    new_change = MOI.MultirowChange(change.variable, sparse)
-    MOI.modify(model, bridge.constraint, new_change)
-    return
-end
-
 """
     abstract type SetMapBridge{T,S2,S1,F,G} <: MultiSetMapBridge{T,S1,G} end
 
diff --git a/test/Bridges/Constraint/test_GreaterToLessBridge.jl b/test/Bridges/Constraint/test_GreaterToLessBridge.jl
index 00a8fb577c..001e4f1743 100644
--- a/test/Bridges/Constraint/test_GreaterToLessBridge.jl
+++ b/test/Bridges/Constraint/test_GreaterToLessBridge.jl
@@ -452,6 +452,47 @@ function test_runtests()
     return
 end
 
+function test_GreaterToLess_modify()
+    inner = MOI.Utilities.Model{Float64}()
+    model = MOI.Bridges.Constraint.GreaterToLess{Float64}(inner)
+    x = MOI.add_variable(model)
+    c = MOI.add_constraint(model, 1.0 * x + 1.0, MOI.GreaterThan(2.0))
+    x_inner = only(MOI.get(inner, MOI.ListOfVariableIndices()))
+    F, S = MOI.ScalarAffineFunction{Float64}, MOI.LessThan{Float64}
+    c_inner = only(MOI.get(inner, MOI.ListOfConstraintIndices{F,S}()))
+    f_inner = MOI.get(inner, MOI.ConstraintFunction(), c_inner)
+    @test isapprox(f_inner, -1.0 * x_inner - 1.0)
+    MOI.modify(model, c, MOI.ScalarCoefficientChange(x, -2.0))
+    f_inner = MOI.get(inner, MOI.ConstraintFunction(), c_inner)
+    @test isapprox(f_inner, 2.0 * x_inner - 1.0)
+    MOI.modify(model, c, MOI.ScalarConstantChange(-3.0))
+    f_inner = MOI.get(inner, MOI.ConstraintFunction(), c_inner)
+    @test isapprox(f_inner, 2.0 * x_inner + 3.0)
+    @test MOI.get(inner, MOI.ConstraintSet(), c_inner) == MOI.LessThan(-2.0)
+    return
+end
+
+function test_NonnegToNonpos_modify()
+    inner = MOI.Utilities.Model{Float64}()
+    model = MOI.Bridges.Constraint.NonnegToNonpos{Float64}(inner)
+    x = MOI.add_variable(model)
+    f = MOI.Utilities.vectorize([1.0 * x + 1.0])
+    c = MOI.add_constraint(model, f, MOI.Nonnegatives(1))
+    x_inner = only(MOI.get(inner, MOI.ListOfVariableIndices()))
+    F, S = MOI.VectorAffineFunction{Float64}, MOI.Nonpositives
+    c_inner = only(MOI.get(inner, MOI.ListOfConstraintIndices{F,S}()))
+    f_inner = MOI.get(inner, MOI.ConstraintFunction(), c_inner)
+    @test isapprox(f_inner, MOI.Utilities.vectorize([-1.0 * x_inner - 1.0]))
+    MOI.modify(model, c, MOI.MultirowChange(x, [(1, -2.0)]))
+    f_inner = MOI.get(inner, MOI.ConstraintFunction(), c_inner)
+    @test isapprox(f_inner, MOI.Utilities.vectorize([2.0 * x_inner - 1.0]))
+    MOI.modify(model, c, MOI.VectorConstantChange([-3.0]))
+    f_inner = MOI.get(inner, MOI.ConstraintFunction(), c_inner)
+    @test isapprox(f_inner, MOI.Utilities.vectorize([2.0 * x_inner + 3.0]))
+    @test MOI.get(inner, MOI.ConstraintSet(), c_inner) == MOI.Nonpositives(1)
+    return
+end
+
 end  # module
 
 TestConstraintFlipSign.runtests()
diff --git a/test/Bridges/General/identity_bridge.jl b/test/Bridges/General/identity_bridge.jl
index 830c49f5cc..75e526f30c 100644
--- a/test/Bridges/General/identity_bridge.jl
+++ b/test/Bridges/General/identity_bridge.jl
@@ -31,6 +31,15 @@ MOI.Bridges.inverse_map_function(::Type{<:IdentityBridge}, func) = func
 MOI.Bridges.adjoint_map_function(::Type{<:IdentityBridge}, func) = func
 MOI.Bridges.inverse_adjoint_map_function(::Type{<:IdentityBridge}, func) = func
 
+function MOI.modify(
+    model::MOI.ModelLike,
+    bridge::ConstraintBridge,
+    change::Union{MOI.ScalarConstantChange,MOI.ScalarCoefficientChange},
+)
+    MOI.modify(model, bridge.constraint, change)
+    return
+end
+
 struct ObjectiveBridge{T} <: MOI.Bridges.Objective.AbstractBridge end
 
 function MOI.Bridges.Objective.bridge_objective(