diff --git a/include/mp/flat/converter_multiobj.h b/include/mp/flat/converter_multiobj.h
index 69fe49e7e..486a62279 100644
--- a/include/mp/flat/converter_multiobj.h
+++ b/include/mp/flat/converter_multiobj.h
@@ -98,11 +98,13 @@ class MOManager {
         objval_last_ = objs.front();           // 0. save emulated obj value
       // @todo 1. check if the solver correctly reports the current emulated obj
       // 2. Let's recompute the original objectives
+      // and the last iteration's objective, TODO: if needed
       const auto& xx = sol.GetVarValues()();
       if (xx.size()) {                         // This can be invoked w/o solution
         objs.resize( MPCD(num_objs()) );
         for (int i=0; i<(int)objs.size(); ++i)
           objs[i] = ComputeValue(MPCD(get_obj(i)), xx);
+        objval_last_ = ComputeValue(obj_new_[i_current_obj_-1], xx);
       }
     }
   }
diff --git a/include/mp/flat/prepro_prod.h b/include/mp/flat/prepro_prod.h
index 06684896c..4e1e701f4 100644
--- a/include/mp/flat/prepro_prod.h
+++ b/include/mp/flat/prepro_prod.h
@@ -90,7 +90,7 @@ class PreproProd
       std::get<2>(tpl) =
           {bnds.lb(), bnds.ub()};
     }
-    std::sort(terms_flt_.begin(), terms_flt_.end(),
+    std::stable_sort(terms_flt_.begin(), terms_flt_.end(),
               [](const auto& tpl1, const auto& tpl2) {
       return std::get<0>(tpl1) < std::get<0>(tpl2);
     });
diff --git a/solvers/mp2nl/mp2nlbackend.cc b/solvers/mp2nl/mp2nlbackend.cc
index caaf0eab5..86d9d81f9 100644
--- a/solvers/mp2nl/mp2nlbackend.cc
+++ b/solvers/mp2nl/mp2nlbackend.cc
@@ -85,11 +85,14 @@ class MP2NLSolverQueryCallbacksImpl
         result.values_[2]
     });
     result.values_[0] = suf_pre.GetVarValues()();
-    result.values_[2] = suf_pre.GetObjValues()();
     result.values_[1] = suf_pre.GetConValues()(CG_Algebraic);
     const auto& suf_log = suf_pre.GetConValues()(CG_Logical);
     result.values_[1].insert(result.values_[1].end(),
                                     suf_log.begin(), suf_log.end());
+    if (be_.multiobj())   // Skip because we compress objectives
+      result.values_[2].clear(); // @todo native multiobj
+    else
+      result.values_[2] = suf_pre.GetObjValues()();
     return result;
   }
 private:
diff --git a/solvers/mp2nl/mp2nlmodelapi.cc b/solvers/mp2nl/mp2nlmodelapi.cc
index d4ab36736..790bedeca 100644
--- a/solvers/mp2nl/mp2nlmodelapi.cc
+++ b/solvers/mp2nl/mp2nlmodelapi.cc
@@ -486,7 +486,7 @@ void MP2NLModelAPI::MarkVars() {
 }
 
 void MP2NLModelAPI::SortVars() {
-  std::sort(mark_data_.var_prior_.begin(), mark_data_.var_prior_.end());
+  std::stable_sort(mark_data_.var_prior_.begin(), mark_data_.var_prior_.end());
   mark_data_.var_order_12_.resize(var_lbs_.size());
   mark_data_.var_order_21_.resize(var_lbs_.size());
   for (auto i=var_lbs_.size(); i--; ) {
@@ -504,7 +504,7 @@ void MP2NLModelAPI::MarkAlgCons() {
 }
 
 void MP2NLModelAPI::SortAlgCons() {
-  std::sort(mark_data_.con_prior_.begin(), mark_data_.con_prior_.end());
+  std::stable_sort(mark_data_.con_prior_.begin(), mark_data_.con_prior_.end());
   mark_data_.con_order_12_.resize(alg_con_info_.size());
   mark_data_.con_order_21_.resize(alg_con_info_.size());
   for (auto i=alg_con_info_.size(); i--; ) {
@@ -1352,6 +1352,7 @@ class MP2NLSolverImpl
    */
   int OnAMPLOptions(const AMPLOptions& ) {
     suf_map_.clear();              // clear for new solution
+    if_suf_data_registered_ = false;
     return 0;
   }
 
@@ -1496,7 +1497,9 @@ class MP2NLSolverImpl
       auto sparse_entry = sr.ReadNext();
       if (sparse_entry.first<0 || sparse_entry.first>=nmax) {
         sr.SetError(NLW2_SOLRead_Bad_Suffix,
-                    "bad suffix element index");
+                    fmt::format(
+          "bad suffix({}, kind={}) element index: {}, should be in [{}, {})",
+                        name, kind, sparse_entry.first, 0, nmax));
         return;
       }
       int i0 = sparse_entry.first;
diff --git a/solvers/mp2nl/mp2nlmodelapi.h b/solvers/mp2nl/mp2nlmodelapi.h
index 37ab06bc0..6f6f1eadb 100644
--- a/solvers/mp2nl/mp2nlmodelapi.h
+++ b/solvers/mp2nl/mp2nlmodelapi.h
@@ -1041,11 +1041,12 @@ class MP2NLModelAPI
   void MarkRangeOrEqn(const LinConRange& lcr) {
     Add2ColSizes(lcr.vars());
     if (lcr.lb() > MinusInfinity()
-        && lcr.ub() < Infinity())
+        && lcr.ub() < Infinity()) {
       if (lcr.lb() < lcr.ub())
         ++mark_data_.n_ranges_;
       else
         ++mark_data_.n_eqns_;
+    }
   }
 
   /// Mark LinConEQ
@@ -1351,20 +1352,38 @@ class MP2NLModelAPI
   public:
     /// Construct
     ItemInfo (BasicItemDispatcher& disp, void* pitem,
-             bool fLogical
+             bool fLogical,
+             bool f_m = 0, LinPartRefOrStorage lpe = {}
              //, StaticItemTypeID iid, ExpressionTypeID eid
              )
-        : disp_(disp), p_item_(pitem), f_logical_(fLogical)
+        : disp_(disp), p_item_(pitem), f_logical_(fLogical),
+        f_marked_(f_m), lin_part_ext_(lpe)
         // no storing, itemID_(iid), exprID_(eid)
     { }
     /// Copy construct
     ItemInfo(const ItemInfo& ii)
-        : ItemInfo(ii.disp_, ii.p_item_, ii.f_logical_) { }
+        : ItemInfo(ii.disp_, ii.p_item_, ii.f_logical_,
+                   ii.f_marked_, ii.lin_part_ext_) { }
     /// operator=
     ItemInfo& operator=(const ItemInfo& ii) {
       assert(&disp_==&ii.disp_);
       p_item_ = ii.p_item_;
       assert(f_logical_==ii.f_logical_);
+      f_marked_ = ii.f_marked_;
+      lin_part_ext_ = ii.lin_part_ext_;
+      return *this;
+    }
+    /// Move construct
+    ItemInfo(ItemInfo&& ii)
+        : ItemInfo(ii.disp_, ii.p_item_, ii.f_logical_,
+                   ii.f_marked_, std::move(ii.lin_part_ext_)) { }
+    /// operator=(&&)
+    ItemInfo& operator=(ItemInfo&& ii) {
+      assert(&disp_==&ii.disp_);
+      p_item_ = ii.p_item_;
+      assert(f_logical_==ii.f_logical_);
+      f_marked_ = ii.f_marked_;
+      lin_part_ext_ = std::move(ii.lin_part_ext_);
       return *this;
     }
     /// Get dispatcher