diff --git a/openmp/docs/design/Runtimes.rst b/openmp/docs/design/Runtimes.rst
--- a/openmp/docs/design/Runtimes.rst
+++ b/openmp/docs/design/Runtimes.rst
@@ -468,7 +468,7 @@
 resources are detected, you may be able to specify additional resources, such as
 NUMA domains and groups of hardware resources that share certain cache levels.
 
-**Basic syntax:** ``num_unitsID[@offset][:attribute] [,num_unitsID[@offset][:attribute]...]``
+**Basic syntax:** ``[num_units|*]ID[@offset][:attribute] [,[num_units|*]ID[@offset][:attribute]...]``
 
 Supported unit IDs are not case-insensitive.
 
@@ -484,6 +484,11 @@
 | ``T`` - thread
 | ``num_units`` specifies the requested number of HW threads per core.
 
+.. note::
+    ``num_units`` can be left out or explicitly specified as ``*`` instead of a positive integer
+    meaning use all specified resources at that level.
+    e.g., ``1s,*c`` means use 1 socket and all the cores on that socket
+
 ``offset`` - (Optional) The number of units to skip.
 
 ``attribute`` - (Optional) An attribute differentiating resources at a particular level. The attributes available to users are:
@@ -554,6 +559,8 @@
   architecture, depending on ``KMP_TOPOLOGY_METHOD`` specified, as hwloc can
   often detect more topology layers than the default method used by the OpenMP
   run-time library.
+* ``*c:eff1@3``: Use all available sockets, skip the first three cores of
+  efficiency 1, and then use the rest of the available cores of efficiency 1.
 
 To see the result of the setting, you can specify ``verbose`` modifier in
 ``KMP_AFFINITY`` environment variable. The OpenMP run-time library will output
diff --git a/openmp/runtime/src/kmp_affinity.h b/openmp/runtime/src/kmp_affinity.h
--- a/openmp/runtime/src/kmp_affinity.h
+++ b/openmp/runtime/src/kmp_affinity.h
@@ -15,6 +15,7 @@
 
 #include "kmp.h"
 #include "kmp_os.h"
+#include <limits>
 
 #if KMP_AFFINITY_SUPPORTED
 #if KMP_USE_HWLOC
@@ -879,6 +880,8 @@
     int offset[MAX_ATTRS];
     kmp_hw_attr_t attr[MAX_ATTRS];
   };
+  // Put parenthesis around max to avoid accidental use of Windows max macro.
+  const static int USE_ALL = (std::numeric_limits<int>::max)();
 
 private:
   int depth;
diff --git a/openmp/runtime/src/kmp_affinity.cpp b/openmp/runtime/src/kmp_affinity.cpp
--- a/openmp/runtime/src/kmp_affinity.cpp
+++ b/openmp/runtime/src/kmp_affinity.cpp
@@ -982,7 +982,8 @@
 
     // Check to see if each layer's num & offset parameters are valid
     max_count = get_ratio(level);
-    if (max_count < 0 || num + offset > max_count) {
+    if (max_count < 0 ||
+        (num != kmp_hw_subset_t::USE_ALL && num + offset > max_count)) {
       bool plural = (num > 1);
       KMP_WARNING(AffHWSubsetManyGeneric,
                   __kmp_hw_get_catalog_string(type, plural));
@@ -1053,7 +1054,8 @@
           int level_above = core_level - 1;
           if (level_above >= 0) {
             max_count = get_ncores_with_attr_per(item.attr[j], level_above);
-            if (max_count <= 0 || num + offset > max_count) {
+            if (max_count <= 0 ||
+                (num != kmp_hw_subset_t::USE_ALL && num + offset > max_count)) {
               kmp_str_buf_t buf;
               __kmp_hw_get_catalog_core_string(item.attr[j], &buf, num > 0);
               KMP_WARNING(AffHWSubsetManyGeneric, buf.str);
@@ -1175,7 +1177,8 @@
           sub_id = core_type_sub_ids.get_sub_id(hw_thread);
         else
           sub_id = core_eff_sub_ids.get_sub_id(hw_thread);
-        if (sub_id < offset || sub_id >= offset + num) {
+        if (sub_id < offset ||
+            (num != kmp_hw_subset_t::USE_ALL && sub_id >= offset + num)) {
           should_be_filtered = true;
           break;
         }
@@ -1183,7 +1186,8 @@
         int num = hw_subset_item.num[0];
         int offset = hw_subset_item.offset[0];
         if (hw_thread.sub_ids[level] < offset ||
-            hw_thread.sub_ids[level] >= offset + num) {
+            (num != kmp_hw_subset_t::USE_ALL &&
+             hw_thread.sub_ids[level] >= offset + num)) {
           should_be_filtered = true;
           break;
         }
diff --git a/openmp/runtime/src/kmp_settings.cpp b/openmp/runtime/src/kmp_settings.cpp
--- a/openmp/runtime/src/kmp_settings.cpp
+++ b/openmp/runtime/src/kmp_settings.cpp
@@ -4978,10 +4978,20 @@
       char *attr_ptr;
       int offset = 0;
       kmp_hw_attr_t attr;
-      int num =
-          atoi(core_components[j]); // each component should start with a number
-      if (num <= 0) {
-        goto err; // only positive integers are valid for count
+      int num;
+      // components may begin with an optional count of the number of resources
+      if (isdigit(*core_components[j])) {
+        num = atoi(core_components[j]);
+        if (num <= 0) {
+          goto err; // only positive integers are valid for count
+        }
+        pos = core_components[j] + strspn(core_components[j], digits);
+      } else if (*core_components[j] == '*') {
+        num = kmp_hw_subset_t::USE_ALL;
+        pos = core_components[j] + 1;
+      } else {
+        num = kmp_hw_subset_t::USE_ALL;
+        pos = core_components[j];
       }
 
       offset_ptr = strchr(core_components[j], '@');
@@ -5016,10 +5026,6 @@
         }
         *attr_ptr = '\0'; // cut the attribute from the component
       }
-      pos = core_components[j] + strspn(core_components[j], digits);
-      if (pos == core_components[j]) {
-        goto err;
-      }
       // detect the component type
       kmp_hw_t type = __kmp_stg_parse_hw_subset_name(pos);
       if (type == KMP_HW_UNKNOWN) {