diff --git a/src/RHEO/compute_rheo_vshift.cpp b/src/RHEO/compute_rheo_vshift.cpp
index 0047521e37..801b65fe3b 100644
--- a/src/RHEO/compute_rheo_vshift.cpp
+++ b/src/RHEO/compute_rheo_vshift.cpp
@@ -81,8 +81,8 @@ void ComputeRHEOVShift::init()
   cutsq = cut * cut;
   cutthird = cut / 3.0;
 
-  multiphase_flag = fix_rheo->shift_multiphase_flag;
-  if (multiphase_flag) {
+  cross_type_flag = fix_rheo->shift_cross_type_flag;
+  if (cross_type_flag) {
     scale = fix_rheo->shift_scale;
     wmin = fix_rheo->shift_wmin;
     cmin = fix_rheo->shift_cmin;
@@ -134,7 +134,7 @@ void ComputeRHEOVShift::compute_peratom()
   if (nmax_store < atom->nmax) {
     memory->grow(vshift, atom->nmax, 3, "rheo:vshift");
 
-    if (multiphase_flag) {
+    if (cross_type_flag) {
       memory->grow(ct, atom->nmax, "rheo:ct");
       memory->grow(cgradt, atom->nmax, 3, "rheo:cgradt");
       memory->grow(wsame, atom->nmax, "rheo:wsame");
@@ -254,7 +254,7 @@ void ComputeRHEOVShift::compute_peratom()
       for (a = 0; a < dim; a++)
         vshift[i][a] = 0.0;
 
-  if (multiphase_flag) correct_interfaces();
+  if (cross_type_flag) correct_interfaces();
 }
 
 /* ---------------------------------------------------------------------- */
@@ -624,7 +624,7 @@ double ComputeRHEOVShift::memory_usage()
 {
   double bytes = 3 * nmax_store * sizeof(double);
 
-  if (multiphase_flag)
+  if (cross_type_flag)
     bytes += 5 * nmax_store * sizeof(double);
 
   return bytes;
diff --git a/src/RHEO/compute_rheo_vshift.h b/src/RHEO/compute_rheo_vshift.h
index 5d763ab008..04512c9740 100644
--- a/src/RHEO/compute_rheo_vshift.h
+++ b/src/RHEO/compute_rheo_vshift.h
@@ -46,7 +46,7 @@ class ComputeRHEOVShift : public Compute {
   int nmax_store, comm_stage;
   double dtv, cut, cutsq, cutthird;
   double scale, wmin, cmin;
-  int surface_flag, interface_flag, multiphase_flag;
+  int surface_flag, interface_flag, cross_type_flag;
   double *rho0;
   double *wsame, *ct, **cgradt;
   int *shift_type;
diff --git a/src/RHEO/fix_rheo.cpp b/src/RHEO/fix_rheo.cpp
index 806ef0873c..06ffa654af 100644
--- a/src/RHEO/fix_rheo.cpp
+++ b/src/RHEO/fix_rheo.cpp
@@ -52,9 +52,9 @@ static const char cite_rheo[] =
 /* ---------------------------------------------------------------------- */
 
 FixRHEO::FixRHEO(LAMMPS *lmp, int narg, char **arg) :
-    Fix(lmp, narg, arg), rho0(nullptr), csq(nullptr), compute_grad(nullptr),
-    compute_kernel(nullptr), compute_interface(nullptr), compute_surface(nullptr),
-    compute_rhosum(nullptr), compute_vshift(nullptr)
+    Fix(lmp, narg, arg), rho0(nullptr), csq(nullptr), shift_type(nullptr),
+    compute_grad(nullptr), compute_kernel(nullptr), compute_interface(nullptr),
+    compute_surface(nullptr), compute_rhosum(nullptr), compute_vshift(nullptr)
 {
   time_integrate = 1;
 
@@ -68,20 +68,18 @@ FixRHEO::FixRHEO(LAMMPS *lmp, int narg, char **arg) :
   shift_flag = 0;
   interface_flag = 0;
   surface_flag = 0;
-  oxidation_flag = 0;
-  self_mass_flag = 0;
   coordination_flag = 0;
-  shift_multiphase_flag = 0;
+
+  rhosum_self_mass_flag = 0;
+  shift_cross_type_flag = 0;
 
   int i;
   int n = atom->ntypes;
   memory->create(rho0, n + 1, "rheo:rho0");
   memory->create(csq, n + 1, "rheo:csq");
-  memory->create(shift_type, n + 1, "rheo:shift_type");
   for (i = 1; i <= n; i++) {
     rho0[i] = 1.0;
     csq[i] = 1.0;
-    shift_type[i] = 1;
   }
 
   if (igroup != 0) error->all(FLERR, "fix rheo command requires group all");
@@ -115,19 +113,26 @@ FixRHEO::FixRHEO(LAMMPS *lmp, int narg, char **arg) :
   while (iarg < narg) {
     if (strcmp(arg[iarg], "shift") == 0) {
       shift_flag = 1;
-    } else if (strcmp(arg[iarg], "shift/multiphase/scale") == 0) {
-      if (iarg + 3 >= narg) utils::missing_cmd_args(FLERR, "fix rheo shift/multiphase/scale", error);
-      shift_multiphase_flag = 1;
-      shift_scale = utils::numeric(FLERR, arg[iarg + 1], false, lmp);
-      shift_wmin = utils::numeric(FLERR, arg[iarg + 2], false, lmp);
-      shift_cmin = utils::numeric(FLERR, arg[iarg + 3], false, lmp);
-      iarg += 3;
-    } else if (strcmp(arg[iarg], "shift/type") == 0) {
-      if (iarg + n >= narg) utils::missing_cmd_args(FLERR, "fix rheo shift/type", error);
-      for (i = 1; i <= n; i++) {
-        shift_type[i] = utils::logical(FLERR, arg[iarg + i], false, lmp);
+      memory->create(shift_type, n + 1, "rheo:shift_type");
+      for (i = 1; i <= n; i++) shift_type[i] = 1;
+      while (iarg < narg) {  // optional sub-arguments
+        if (strcmp(arg[iarg], "scale/cross/type") == 0) {
+          if (iarg + 3 >= narg) utils::missing_cmd_args(FLERR, "fix rheo shift scale/cross/type", error);
+          shift_cross_type_flag = 1;
+          shift_scale = utils::numeric(FLERR, arg[iarg + 1], false, lmp);
+          shift_wmin = utils::numeric(FLERR, arg[iarg + 2], false, lmp);
+          shift_cmin = utils::numeric(FLERR, arg[iarg + 3], false, lmp);
+          iarg += 3;
+        } else if (strcmp(arg[iarg], "exclude/type") == 0) {
+          if (iarg + n >= narg) utils::missing_cmd_args(FLERR, "fix rheo shift exclude/type", error);
+          for (i = 1; i <= n; i++)
+            shift_type[i] = utils::logical(FLERR, arg[iarg + i], false, lmp);
+          iarg += n;
+        } else {
+          break;
+        }
+        iarg += 1;
       }
-      iarg += n;
     } else if (strcmp(arg[iarg], "thermal") == 0) {
       thermal_flag = 1;
     } else if (strcmp(arg[iarg], "surface/detection") == 0) {
@@ -149,8 +154,14 @@ FixRHEO::FixRHEO(LAMMPS *lmp, int narg, char **arg) :
       interface_flag = 1;
     } else if (strcmp(arg[iarg], "rho/sum") == 0) {
       rhosum_flag = 1;
-    } else if (strcmp(arg[iarg], "self/mass") == 0) {
-      self_mass_flag = 1;
+      while (iarg < narg) {  // optional sub-arguments
+        if (strcmp(arg[iarg], "self/mass") == 0) {
+          rhosum_self_mass_flag = 1;
+        } else {
+          break;
+        }
+        iarg += 1;
+      }
     } else if (strcmp(arg[iarg], "density") == 0) {
       if (iarg + n >= narg) utils::missing_cmd_args(FLERR, "fix rheo density", error);
       for (i = 1; i <= n; i++) rho0[i] = utils::numeric(FLERR, arg[iarg + i], false, lmp);
@@ -168,12 +179,6 @@ FixRHEO::FixRHEO(LAMMPS *lmp, int narg, char **arg) :
     iarg += 1;
   }
 
-  if ((!shift_flag) && shift_multiphase_flag)
-    error->all(FLERR, "Cannot use shift/multiphase/scale without shifting");
-
-  if (self_mass_flag && (!rhosum_flag))
-    error->all(FLERR, "Cannot use self/mass setting without rho/sum");
-
 #if 0
   if (lmp->citeme) lmp->citeme->add(cite_rheo);
 #endif
@@ -212,7 +217,7 @@ void FixRHEO::post_constructor()
 
   if (rhosum_flag) {
     compute_rhosum = dynamic_cast<ComputeRHEORhoSum *>(
-        modify->add_compute(fmt::format("rheo_rhosum all RHEO/RHO/SUM {}", self_mass_flag)));
+        modify->add_compute(fmt::format("rheo_rhosum all RHEO/RHO/SUM {}", rhosum_self_mass_flag)));
     compute_rhosum->fix_rheo = this;
   }
 
diff --git a/src/RHEO/fix_rheo.h b/src/RHEO/fix_rheo.h
index acad9f0321..aa80bc938e 100644
--- a/src/RHEO/fix_rheo.h
+++ b/src/RHEO/fix_rheo.h
@@ -41,23 +41,25 @@ class FixRHEO : public Fix {
   // Model parameters
   double cut;
   double *rho0, *csq;
-  int *shift_type;
-  int self_mass_flag;
   int zmin_kernel, zmin_surface, zmin_splash;
   int kernel_style, surface_style;
   double divr_surface;
+
+  // Settings flags
+  int thermal_flag;
+  int rhosum_flag;
+  int interface_flag;
+  int surface_flag;
+  int shift_flag;
+  int coordination_flag;
+
+  // Optional sub-flags/parameters
+  int rhosum_self_mass_flag;
+  int *shift_type;
+  int shift_cross_type_flag;
   double shift_scale, shift_wmin, shift_cmin;
 
   // Accessory fixes/computes
-  int thermal_flag;
-  int rhosum_flag;
-  int shift_flag;
-  int interface_flag;
-  int surface_flag;
-  int oxidation_flag;
-  int coordination_flag;
-  int shift_multiphase_flag;
-
   int viscosity_fix_defined;
   int pressure_fix_defined;
   int thermal_fix_defined;