diff --git a/modules/lang-expression/src/internalClusterTest/java/org/opensearch/script/expression/MoreExpressionIT.java b/modules/lang-expression/src/internalClusterTest/java/org/opensearch/script/expression/MoreExpressionIT.java
index 4ae3be72a8ab3..80974b3b3f104 100644
--- a/modules/lang-expression/src/internalClusterTest/java/org/opensearch/script/expression/MoreExpressionIT.java
+++ b/modules/lang-expression/src/internalClusterTest/java/org/opensearch/script/expression/MoreExpressionIT.java
@@ -504,10 +504,6 @@ public void testInvalidFieldMember() {
     }
 
     public void testSpecialValueVariable() throws Exception {
-        assumeFalse(
-            "Concurrent search case muted pending fix: https://github.com/opensearch-project/OpenSearch/issues/10079",
-            internalCluster().clusterService().getClusterSettings().get(CLUSTER_CONCURRENT_SEGMENT_SEARCH_SETTING)
-        );
         // i.e. _value for aggregations
         createIndex("test");
         ensureGreen("test");
diff --git a/modules/lang-expression/src/main/java/org/opensearch/script/expression/ExpressionAggregationScript.java b/modules/lang-expression/src/main/java/org/opensearch/script/expression/ExpressionAggregationScript.java
index 5eebb9c4d60ad..a2af636ffdc8a 100644
--- a/modules/lang-expression/src/main/java/org/opensearch/script/expression/ExpressionAggregationScript.java
+++ b/modules/lang-expression/src/main/java/org/opensearch/script/expression/ExpressionAggregationScript.java
@@ -53,9 +53,9 @@ class ExpressionAggregationScript implements AggregationScript.LeafFactory {
     final SimpleBindings bindings;
     final DoubleValuesSource source;
     final boolean needsScore;
-    final ReplaceableConstDoubleValueSource specialValue; // _value
+    final PerThreadReplaceableConstDoubleValueSource specialValue; // _value
 
-    ExpressionAggregationScript(Expression e, SimpleBindings b, boolean n, ReplaceableConstDoubleValueSource v) {
+    ExpressionAggregationScript(Expression e, SimpleBindings b, boolean n, PerThreadReplaceableConstDoubleValueSource v) {
         exprScript = e;
         bindings = b;
         source = exprScript.getDoubleValuesSource(bindings);
diff --git a/modules/lang-expression/src/main/java/org/opensearch/script/expression/ExpressionScriptEngine.java b/modules/lang-expression/src/main/java/org/opensearch/script/expression/ExpressionScriptEngine.java
index 11b2e20eea523..5629b3b4a6972 100644
--- a/modules/lang-expression/src/main/java/org/opensearch/script/expression/ExpressionScriptEngine.java
+++ b/modules/lang-expression/src/main/java/org/opensearch/script/expression/ExpressionScriptEngine.java
@@ -316,14 +316,14 @@ private static AggregationScript.LeafFactory newAggregationScript(
         // instead of complicating SimpleBindings (which should stay simple)
         SimpleBindings bindings = new SimpleBindings();
         boolean needsScores = false;
-        ReplaceableConstDoubleValueSource specialValue = null;
+        PerThreadReplaceableConstDoubleValueSource specialValue = null;
         for (String variable : expr.variables) {
             try {
                 if (variable.equals("_score")) {
                     bindings.add("_score", DoubleValuesSource.SCORES);
                     needsScores = true;
                 } else if (variable.equals("_value")) {
-                    specialValue = new ReplaceableConstDoubleValueSource();
+                    specialValue = new PerThreadReplaceableConstDoubleValueSource();
                     bindings.add("_value", specialValue);
                     // noop: _value is special for aggregations, and is handled in ExpressionScriptBindings
                     // TODO: if some uses it in a scoring expression, they will get a nasty failure when evaluating...need a
@@ -388,7 +388,7 @@ private static ScoreScript.LeafFactory newScoreScript(Expression expr, SearchLoo
         // NOTE: if we need to do anything complicated with bindings in the future, we can just extend Bindings,
         // instead of complicating SimpleBindings (which should stay simple)
         SimpleBindings bindings = new SimpleBindings();
-        ReplaceableConstDoubleValueSource specialValue = null;
+        PerThreadReplaceableConstDoubleValueSource specialValue = null;
         boolean needsScores = false;
         for (String variable : expr.variables) {
             try {
@@ -396,7 +396,7 @@ private static ScoreScript.LeafFactory newScoreScript(Expression expr, SearchLoo
                     bindings.add("_score", DoubleValuesSource.SCORES);
                     needsScores = true;
                 } else if (variable.equals("_value")) {
-                    specialValue = new ReplaceableConstDoubleValueSource();
+                    specialValue = new PerThreadReplaceableConstDoubleValueSource();
                     bindings.add("_value", specialValue);
                     // noop: _value is special for aggregations, and is handled in ExpressionScriptBindings
                     // TODO: if some uses it in a scoring expression, they will get a nasty failure when evaluating...need a
diff --git a/modules/lang-expression/src/main/java/org/opensearch/script/expression/ReplaceableConstDoubleValueSource.java b/modules/lang-expression/src/main/java/org/opensearch/script/expression/PerThreadReplaceableConstDoubleValueSource.java
similarity index 62%
rename from modules/lang-expression/src/main/java/org/opensearch/script/expression/ReplaceableConstDoubleValueSource.java
rename to modules/lang-expression/src/main/java/org/opensearch/script/expression/PerThreadReplaceableConstDoubleValueSource.java
index 28e4707a07192..40bb957c248f2 100644
--- a/modules/lang-expression/src/main/java/org/opensearch/script/expression/ReplaceableConstDoubleValueSource.java
+++ b/modules/lang-expression/src/main/java/org/opensearch/script/expression/PerThreadReplaceableConstDoubleValueSource.java
@@ -39,20 +39,25 @@
 import org.apache.lucene.search.IndexSearcher;
 
 import java.io.IOException;
+import java.util.Map;
+import java.util.concurrent.ConcurrentHashMap;
 
 /**
- * A {@link DoubleValuesSource} which has a stub {@link DoubleValues} that holds a dynamically replaceable constant double.
+ * A {@link DoubleValuesSource} which has a stub {@link DoubleValues} that holds a dynamically replaceable constant double. This is made
+ * thread-safe for concurrent segment search use case by keeping the {@link DoubleValues} per thread. Any update to the value happens in
+ * thread specific {@link DoubleValuesSource} instance.
  */
-final class ReplaceableConstDoubleValueSource extends DoubleValuesSource {
-    final ReplaceableConstDoubleValues fv;
+final class PerThreadReplaceableConstDoubleValueSource extends DoubleValuesSource {
+    // Multiple slices can be processed by same thread but that will be sequential, so keeping per thread is fine
+    final Map<Long, ReplaceableConstDoubleValues> perThreadDoubleValues;
 
-    ReplaceableConstDoubleValueSource() {
-        fv = new ReplaceableConstDoubleValues();
+    PerThreadReplaceableConstDoubleValueSource() {
+        perThreadDoubleValues = new ConcurrentHashMap<>();
     }
 
     @Override
     public DoubleValues getValues(LeafReaderContext ctx, DoubleValues scores) throws IOException {
-        return fv;
+        return perThreadDoubleValues.computeIfAbsent(Thread.currentThread().getId(), threadId -> new ReplaceableConstDoubleValues());
     }
 
     @Override
@@ -62,7 +67,11 @@ public boolean needsScores() {
 
     @Override
     public Explanation explain(LeafReaderContext ctx, int docId, Explanation scoreExplanation) throws IOException {
-        if (fv.advanceExact(docId)) return Explanation.match((float) fv.doubleValue(), "ReplaceableConstDoubleValues");
+        final ReplaceableConstDoubleValues currentFv = perThreadDoubleValues.computeIfAbsent(
+            Thread.currentThread().getId(),
+            threadId -> new ReplaceableConstDoubleValues()
+        );
+        if (currentFv.advanceExact(docId)) return Explanation.match((float) currentFv.doubleValue(), "ReplaceableConstDoubleValues");
         else return Explanation.noMatch("ReplaceableConstDoubleValues");
     }
 
@@ -77,7 +86,11 @@ public int hashCode() {
     }
 
     public void setValue(double v) {
-        fv.setValue(v);
+        final ReplaceableConstDoubleValues currentFv = perThreadDoubleValues.computeIfAbsent(
+            Thread.currentThread().getId(),
+            threadId -> new ReplaceableConstDoubleValues()
+        );
+        currentFv.setValue(v);
     }
 
     @Override