diff --git a/src/MOI_wrapper.jl b/src/MOI_wrapper.jl
index 2d1d8135..a6ff81eb 100644
--- a/src/MOI_wrapper.jl
+++ b/src/MOI_wrapper.jl
@@ -209,9 +209,11 @@ end
 function MOI.copy_to(dest::DualOptimizer, src::MOI.ModelLike)
     dualize(src, dest.dual_problem)
     idx_map = MOI.Utilities.IndexMap()
-    for vi in MOI.get(src, MOI.ListOfVariableIndices())
+    vis_src = MOI.get(src, MOI.ListOfVariableIndices())
+    for vi in vis_src
         setindex!(idx_map, vi, vi)
     end
+    MOI.Utilities.pass_attributes(dest, src, idx_map, vis_src)
     for (F, S) in MOI.get(src, MOI.ListOfConstraintTypesPresent())
         for con in MOI.get(src, MOI.ListOfConstraintIndices{F,S}())
             setindex!(idx_map, con, con)
@@ -322,9 +324,66 @@ function _get_at_index(
     return _get(optimizer, attr, ci_primal, ci_dual)[idx]
 end
 
+_minus(::Nothing) = nothing
+_minus(x) = -x
+
+function _dual_attribute(attr::Union{MOI.VariablePrimal,MOI.ConstraintPrimal})
+    return MOI.ConstraintDual(attr.result_index)
+end
+
+function _dual_attribute(
+    ::Union{MOI.VariablePrimalStart,MOI.ConstraintPrimalStart},
+)
+    return MOI.ConstraintDualStart()
+end
+
+function _dual_attribute(attr::MOI.ConstraintDual)
+    return MOI.ConstraintPrimal(attr.result_index)
+end
+
+function _dual_attribute(::MOI.ConstraintDualStart)
+    return MOI.ConstraintPrimalStart()
+end
+
+function _variable_dual_attribute(attr::MOI.ConstraintDual)
+    return MOI.VariablePrimal(attr.result_index)
+end
+
+function _variable_dual_attribute(::MOI.ConstraintDualStart)
+    return MOI.VariablePrimalStart()
+end
+
+function MOI.supports(
+    ::DualOptimizer,
+    ::MOI.VariablePrimalStart,
+    ::Type{MOI.VariableIndex},
+)
+    return true
+end
+
+function MOI.set(
+    optimizer::DualOptimizer,
+    attr::MOI.VariablePrimalStart,
+    vi::MOI.VariableIndex,
+    value,
+)
+    primal_dual_map = optimizer.dual_problem.primal_dual_map
+    if vi in keys(primal_dual_map.constrained_var_idx)
+        msg = "Setting starting value for variables constrained at creation is not supported yet"
+        throw(MOI.SetAttributeNotAllowed(attr, msg))
+    end
+    MOI.set(
+        optimizer.dual_problem.dual_model,
+        _dual_attribute(attr),
+        get_ci_dual_problem(optimizer, vi),
+        _minus(value),
+    )
+    return
+end
+
 function MOI.get(
     optimizer::DualOptimizer,
-    ::MOI.VariablePrimal,
+    attr::Union{MOI.VariablePrimal,MOI.VariablePrimalStart},
     vi::MOI.VariableIndex,
 )
     primal_dual_map = optimizer.dual_problem.primal_dual_map
@@ -333,23 +392,58 @@ function MOI.get(
         ci_dual = primal_dual_map.constrained_var_dual[ci_primal]
         return _get_at_index(
             optimizer,
-            MOI.ConstraintDual(),
+            _dual_attribute(attr),
             ci_primal,
             ci_dual,
             idx,
         )
-    else
-        return -MOI.get(
-            optimizer.dual_problem.dual_model,
-            MOI.ConstraintDual(),
-            get_ci_dual_problem(optimizer, vi),
-        )
     end
+    ret = MOI.get(
+        optimizer.dual_problem.dual_model,
+        _dual_attribute(attr),
+        get_ci_dual_problem(optimizer, vi),
+    )
+    if ret === nothing
+        return ret
+    end
+    return -ret
+end
+
+function MOI.supports(
+    optimizer::DualOptimizer,
+    attr::MOI.ConstraintDualStart,
+    ::Type{<:MOI.ConstraintIndex},
+)
+    return MOI.supports(
+        optimizer.dual_problem.dual_model,
+        _variable_dual_attribute(attr),
+        MOI.VariableIndex,
+    )
+end
+
+function MOI.set(
+    optimizer::DualOptimizer,
+    attr::MOI.ConstraintDualStart,
+    ci::MOI.ConstraintIndex,
+    value,
+)
+    primal_dual_map = optimizer.dual_problem.primal_dual_map
+    if ci in keys(primal_dual_map.constrained_var_dual)
+        msg = "Setting starting value for variables constrained at creation is not supported yet"
+        throw(MOI.SetAttributeNotAllowed(attr, msg))
+    end
+    MOI.set(
+        optimizer.dual_problem.dual_model,
+        _variable_dual_attribute(attr),
+        get_vi_dual_problem(optimizer, ci),
+        value,
+    )
+    return
 end
 
 function MOI.get(
     optimizer::DualOptimizer,
-    attr::MOI.ConstraintDual,
+    attr::Union{MOI.ConstraintDual,MOI.ConstraintDualStart},
     ci::MOI.ConstraintIndex{F,S},
 ) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
     primal_dual_map = optimizer.dual_problem.primal_dual_map
@@ -361,7 +455,7 @@ function MOI.get(
             ) do vi
                 return MOI.get(
                     optimizer.dual_problem.dual_model,
-                    MOI.VariablePrimal(),
+                    _variable_dual_attribute(attr),
                     vi,
                 )
             end
@@ -373,13 +467,13 @@ function MOI.get(
         )
         return MOI.get(
             optimizer.dual_problem.dual_model,
-            MOI.ConstraintPrimal(),
+            _dual_attribute(attr),
             ci_dual,
         ) - MOI.constant(set)
     else
         return MOI.get(
             optimizer.dual_problem.dual_model,
-            MOI.VariablePrimal(),
+            _variable_dual_attribute(attr),
             get_vi_dual_problem(optimizer, ci),
         )
     end
@@ -387,7 +481,7 @@ end
 
 function MOI.get(
     optimizer::DualOptimizer,
-    ::MOI.ConstraintDual,
+    attr::Union{MOI.ConstraintDual,MOI.ConstraintDualStart},
     ci::MOI.ConstraintIndex{F,S},
 ) where {F<:MOI.AbstractVectorFunction,S<:MOI.AbstractVectorSet}
     primal_dual_map = optimizer.dual_problem.primal_dual_map
@@ -399,35 +493,74 @@ function MOI.get(
             ) do vi
                 return MOI.get(
                     optimizer.dual_problem.dual_model,
-                    MOI.VariablePrimal(),
+                    _variable_dual_attribute(attr),
                     vi,
                 )
             end
         end
         return MOI.get(
             optimizer.dual_problem.dual_model,
-            MOI.ConstraintPrimal(),
+            _dual_attribute(attr),
             primal_dual_map.constrained_var_dual[ci],
         )
     else
         return MOI.get.(
             optimizer.dual_problem.dual_model,
-            MOI.VariablePrimal(),
+            _variable_dual_attribute(attr),
             get_vis_dual_problem(optimizer, ci),
         )
     end
 end
 
+function MOI.supports(
+    ::DualOptimizer,
+    attr::MOI.ConstraintPrimalStart,
+    C::Type{<:MOI.ConstraintIndex},
+)
+    return MOI.supports(
+        optimizer.dual_problem.dual_model,
+        _dual_attribute(attr),
+        C,
+    )
+end
+
+function MOI.set(
+    optimizer::DualOptimizer,
+    attr::MOI.ConstraintPrimalStart,
+    ci::MOI.ConstraintIndex{F},
+    value,
+) where {F<:MOI.AbstractScalarFunction}
+    primal_dual_map = optimizer.dual_problem.primal_dual_map
+    if ci in keys(primal_dual_map.constrained_var_dual)
+        error(
+            "Setting starting value for variables constrained at creation is not supported yet",
+        )
+    elseif haskey(primal_dual_map.primal_con_dual_con, ci)
+        # If it has no key then there is no dual constraint
+        ci_dual_problem = get_ci_dual_problem(optimizer, ci)
+        if !isnothing(value) && (F <: MOI.AbstractScalarFunction)
+            value -= get_primal_ci_constant(optimizer, ci)
+        end
+        MOI.set(
+            optimizer.dual_problem.dual_model,
+            _dual_attribute(attr),
+            ci_dual_problem,
+            value,
+        )
+    end
+    return
+end
+
 function MOI.get(
     optimizer::DualOptimizer,
-    ::MOI.ConstraintPrimal,
+    attr::Union{MOI.ConstraintPrimal,MOI.ConstraintPrimalStart},
     ci::MOI.ConstraintIndex{F,S},
 ) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
     primal_dual_map = optimizer.dual_problem.primal_dual_map
     if ci in keys(primal_dual_map.constrained_var_dual)
         return _get(
             optimizer,
-            MOI.ConstraintDual(),
+            _dual_attribute(attr),
             ci,
             primal_dual_map.constrained_var_dual[ci],
         )
@@ -440,7 +573,7 @@ function MOI.get(
         ci_dual_problem = get_ci_dual_problem(optimizer, ci)
         return MOI.get(
             optimizer.dual_problem.dual_model,
-            MOI.ConstraintDual(),
+            _dual_attribute(attr),
             ci_dual_problem,
         ) - primal_ci_constant
     end
@@ -448,14 +581,14 @@ end
 
 function MOI.get(
     optimizer::DualOptimizer{T},
-    ::MOI.ConstraintPrimal,
+    attr::Union{MOI.ConstraintPrimal,MOI.ConstraintPrimalStart},
     ci::MOI.ConstraintIndex{F,S},
 ) where {T,F<:MOI.AbstractVectorFunction,S<:MOI.AbstractVectorSet}
     primal_dual_map = optimizer.dual_problem.primal_dual_map
     if ci in keys(primal_dual_map.constrained_var_dual)
         return _get(
             optimizer,
-            MOI.ConstraintDual(),
+            _dual_attribute(attr),
             ci,
             primal_dual_map.constrained_var_dual[ci],
         )
@@ -469,7 +602,7 @@ function MOI.get(
         ci_dual_problem = get_ci_dual_problem(optimizer, ci)
         return MOI.get(
             optimizer.dual_problem.dual_model,
-            MOI.ConstraintDual(),
+            _dual_attribute(attr),
             ci_dual_problem,
         )
     end
@@ -494,20 +627,20 @@ function dual_status(term::MOI.TerminationStatusCode)
     return term
 end
 
-function MOI.get(optimizer::DualOptimizer, ::MOI.ObjectiveValue)
-    return MOI.get(optimizer.dual_problem.dual_model, MOI.DualObjectiveValue())
+function MOI.get(optimizer::DualOptimizer, attr::MOI.ObjectiveValue)
+    return MOI.get(optimizer.dual_problem.dual_model, MOI.DualObjectiveValue(attr.result_index))
 end
 
-function MOI.get(optimizer::DualOptimizer, ::MOI.DualObjectiveValue)
-    return MOI.get(optimizer.dual_problem.dual_model, MOI.ObjectiveValue())
+function MOI.get(optimizer::DualOptimizer, attr::MOI.DualObjectiveValue)
+    return MOI.get(optimizer.dual_problem.dual_model, MOI.ObjectiveValue(attr.result_index))
 end
 
-function MOI.get(optimizer::DualOptimizer, ::MOI.PrimalStatus)
-    return MOI.get(optimizer.dual_problem.dual_model, MOI.DualStatus())
+function MOI.get(optimizer::DualOptimizer, attr::MOI.PrimalStatus)
+    return MOI.get(optimizer.dual_problem.dual_model, MOI.DualStatus(attr.result_index))
 end
 
-function MOI.get(optimizer::DualOptimizer, ::MOI.DualStatus)
-    return MOI.get(optimizer.dual_problem.dual_model, MOI.PrimalStatus())
+function MOI.get(optimizer::DualOptimizer, attr::MOI.DualStatus)
+    return MOI.get(optimizer.dual_problem.dual_model, MOI.PrimalStatus(attr.result_index))
 end
 
 function MOI.set(
diff --git a/test/Tests/test_MOI_wrapper.jl b/test/Tests/test_MOI_wrapper.jl
index c8741a4a..cfa86fc5 100644
--- a/test/Tests/test_MOI_wrapper.jl
+++ b/test/Tests/test_MOI_wrapper.jl
@@ -127,4 +127,18 @@
                   DualOptimizer{Float32,Caching_OptimizerType}
         end
     end
+
+    @testset "Start" begin
+        model = MOI.Utilities.UniversalFallback(TestModel{Float64}())
+        x = MOI.add_variable(model)
+        c = MOI.add_constraint(model, 2.0 * x, MOI.GreaterThan(0.0))
+        MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+        MOI.set(model, MOI.VariablePrimalStart(), x, 1.0)
+        MOI.set(model, MOI.ConstraintPrimalStart(), c, 3.0)
+        MOI.set(model, MOI.ConstraintDualStart(), c, 4.0)
+        dual_problem = Dualization.DualProblem{Float64}(TestModel{Float64}())
+        OptimizerType = typeof(dual_problem.dual_model)
+        dual = DualOptimizer{Float64,OptimizerType}(dual_problem)
+        index_map = MOI.copy_to(dual, model)
+    end
 end