diff --git a/rest-api-spec/src/main/resources/rest-api-spec/test/search.aggregation/370_multi_terms.yml b/rest-api-spec/src/main/resources/rest-api-spec/test/search.aggregation/370_multi_terms.yml
index 7db5f31d8e761..f9354db46a384 100644
--- a/rest-api-spec/src/main/resources/rest-api-spec/test/search.aggregation/370_multi_terms.yml
+++ b/rest-api-spec/src/main/resources/rest-api-spec/test/search.aggregation/370_multi_terms.yml
@@ -760,3 +760,138 @@ setup:
   - match: { aggregations.histo.buckets.2.key_as_string: "2022-03-25T00:00:00.000Z" }
   - match: { aggregations.histo.buckets.2.m_terms.buckets.0.key: [ "a", "127.0.0.1" ] }
   - match: { aggregations.histo.buckets.2.m_terms.buckets.1.key: [ "b", "127.0.0.1" ] }
+
+---
+"multi_terms bucket and multiple orders test":
+  - skip:
+      version: "- 2.0.99"
+      reason:  multi_terms aggregation is introduced in 2.1.0
+
+  - do:
+      bulk:
+        index: test_1
+        refresh: true
+        body:
+          - '{"index": {}}'
+          - '{"str": "a", "integer": 1, "double": 1234.5, "boolean": true}'
+          - '{"index": {}}'
+          - '{"str": "a", "integer": 2, "double": 5678.9, "boolean": true}'
+          - '{"index": {}}'
+          - '{"str": "a", "integer": 1, "double": 123.4, "boolean": false}'
+          - '{"index": {}}'
+          - '{"str": "a", "integer": 2, "double": 456.7, "boolean": false}'
+          - '{"index": {}}'
+          - '{"str": "b", "integer": 3, "double": 1234.5, "boolean": true}'
+          - '{"index": {}}'
+          - '{"str": "b", "integer": 4, "double": 5678.9, "boolean": true}'
+          - '{"index": {}}'
+          - '{"str": "b", "integer": 3, "double": 234.5, "boolean": false}'
+          - '{"index": {}}'
+          - '{"str": "b", "integer": 4, "double": 456.7, "boolean": false}'
+
+  - do:
+      search:
+        index: test_1
+        size: 0
+        body:
+          aggs:
+            m_terms:
+              multi_terms:
+                terms:
+                  - field: str
+                  - field: boolean
+                order:
+                  - max_int: desc
+                  - min_double: asc
+              aggs:
+                max_int:
+                  max:
+                    field: integer
+                min_double:
+                  min:
+                    field: double
+
+  - length: { aggregations.m_terms.buckets: 4 }
+  - match: { aggregations.m_terms.buckets.0.key: ["b", false] }
+  - match: { aggregations.m_terms.buckets.0.key_as_string: "b|false" }
+  - match: { aggregations.m_terms.buckets.0.doc_count: 2 }
+  - match: { aggregations.m_terms.buckets.0.max_int.value: 4.0 }
+  - match: { aggregations.m_terms.buckets.0.min_double.value: 234.5 }
+  - match: { aggregations.m_terms.buckets.1.key: ["b", true] }
+  - match: { aggregations.m_terms.buckets.1.key_as_string: "b|true" }
+  - match: { aggregations.m_terms.buckets.1.doc_count: 2 }
+  - match: { aggregations.m_terms.buckets.1.max_int.value: 4.0 }
+  - match: { aggregations.m_terms.buckets.1.min_double.value: 1234.5 }
+  - match: { aggregations.m_terms.buckets.2.key: [ "a", false ] }
+  - match: { aggregations.m_terms.buckets.2.key_as_string: "a|false" }
+  - match: { aggregations.m_terms.buckets.2.doc_count: 2 }
+  - match: { aggregations.m_terms.buckets.2.max_int.value: 2.0 }
+  - match: { aggregations.m_terms.buckets.2.min_double.value: 123.4 }
+  - match: { aggregations.m_terms.buckets.3.key: [ "a", true ] }
+  - match: { aggregations.m_terms.buckets.3.key_as_string: "a|true" }
+  - match: { aggregations.m_terms.buckets.3.doc_count: 2 }
+  - match: { aggregations.m_terms.buckets.3.max_int.value: 2.0 }
+  - match: { aggregations.m_terms.buckets.3.min_double.value: 1234.5 }
+
+---
+"multi_terms bucket and multiple orders with size test":
+  - skip:
+      version: "- 2.0.99"
+      reason:  multi_terms aggregation is introduced in 2.1.0
+
+  - do:
+      bulk:
+        index: test_1
+        refresh: true
+        body:
+          - '{"index": {}}'
+          - '{"str": "a", "integer": 1, "double": 1234.5, "boolean": true}'
+          - '{"index": {}}'
+          - '{"str": "a", "integer": 2, "double": 5678.9, "boolean": true}'
+          - '{"index": {}}'
+          - '{"str": "a", "integer": 1, "double": 123.4, "boolean": false}'
+          - '{"index": {}}'
+          - '{"str": "a", "integer": 2, "double": 456.7, "boolean": false}'
+          - '{"index": {}}'
+          - '{"str": "b", "integer": 3, "double": 1234.5, "boolean": true}'
+          - '{"index": {}}'
+          - '{"str": "b", "integer": 4, "double": 5678.9, "boolean": true}'
+          - '{"index": {}}'
+          - '{"str": "b", "integer": 3, "double": 234.5, "boolean": false}'
+          - '{"index": {}}'
+          - '{"str": "b", "integer": 4, "double": 456.7, "boolean": false}'
+
+  - do:
+      search:
+        index: test_1
+        size: 0
+        body:
+          aggs:
+            m_terms:
+              multi_terms:
+                terms:
+                  - field: str
+                  - field: boolean
+                order:
+                  - max_int: desc
+                  - min_double: asc
+                size: 2
+              aggs:
+                max_int:
+                  max:
+                    field: integer
+                min_double:
+                  min:
+                    field: double
+
+  - length: { aggregations.m_terms.buckets: 2 }
+  - match: { aggregations.m_terms.buckets.0.key: ["b", false] }
+  - match: { aggregations.m_terms.buckets.0.key_as_string: "b|false" }
+  - match: { aggregations.m_terms.buckets.0.doc_count: 2 }
+  - match: { aggregations.m_terms.buckets.0.max_int.value: 4.0 }
+  - match: { aggregations.m_terms.buckets.0.min_double.value: 234.5 }
+  - match: { aggregations.m_terms.buckets.1.key: ["b", true] }
+  - match: { aggregations.m_terms.buckets.1.key_as_string: "b|true" }
+  - match: { aggregations.m_terms.buckets.1.doc_count: 2 }
+  - match: { aggregations.m_terms.buckets.1.max_int.value: 4.0 }
+  - match: { aggregations.m_terms.buckets.1.min_double.value: 1234.5 }
diff --git a/server/src/main/java/org/opensearch/search/aggregations/bucket/terms/MultiTermsAggregationBuilder.java b/server/src/main/java/org/opensearch/search/aggregations/bucket/terms/MultiTermsAggregationBuilder.java
index c711b140be192..fb588a04cf93c 100644
--- a/server/src/main/java/org/opensearch/search/aggregations/bucket/terms/MultiTermsAggregationBuilder.java
+++ b/server/src/main/java/org/opensearch/search/aggregations/bucket/terms/MultiTermsAggregationBuilder.java
@@ -51,10 +51,15 @@
  *           },{
  *             "field": "host"
  *           }],
- *           "order": {"max-cpu": "desc"}
+ *           "order": [{
+ *             "max-cpu": "desc"
+ *           },{
+ *             "max-memory": "desc"
+ *           }]
  *         },
  *         "aggs": {
- *           "max-cpu": { "max": { "field": "cpu" } }
+ *           "max-cpu": { "max": { "field": "cpu" } },
+ *           "max-memory": { "max": { "field": "memory" } }
  *         }
  *       }
  *     }
@@ -80,6 +85,9 @@
  *           "doc_count": 2,
  *           "max-cpu": {
  *             "value": 90.0
+ *           },
+ *           "max-memory": {
+ *             "value": 80.0
  *           }
  *         },
  *         {
@@ -91,6 +99,9 @@
  *           "doc_count": 2,
  *           "max-cpu": {
  *             "value": 70.0
+ *           },
+ *           "max-memory": {
+ *             "value": 90.0
  *           }
  *         }
  *       ]