diff --git a/java/ql/lib/semmle/code/Location.qll b/java/ql/lib/semmle/code/Location.qll
index 14fc7a995328..7265164e8e15 100644
--- a/java/ql/lib/semmle/code/Location.qll
+++ b/java/ql/lib/semmle/code/Location.qll
@@ -8,6 +8,7 @@ module;
 
 import FileSystem
 import semmle.code.java.Element
+private import semmle.code.java.Overlay
 private import semmle.code.SMAP
 
 /** Holds if element `e` has name `name`. */
@@ -221,3 +222,16 @@ private predicate fixedHasLocation(Top l, Location loc, File f) {
   not hasSourceLocation(l, _, _) and
   locations_default(loc, f, _, _, _, _)
 }
+
+overlay[local]
+private predicate discardableLocation(string file, @location l) {
+  not isOverlay() and
+  file = getRawFileForLoc(l) and
+  not exists(@file f | hasLocation(f, l))
+}
+
+/** Discard base locations in files fully extracted in the overlay. */
+overlay[discard_entity]
+private predicate discardLocation(@location l) {
+  exists(string file | discardableLocation(file, l) and extractedInOverlay(file))
+}
diff --git a/java/ql/lib/semmle/code/java/Expr.qll b/java/ql/lib/semmle/code/java/Expr.qll
index 182bf5b7001f..cafffae52bd2 100644
--- a/java/ql/lib/semmle/code/java/Expr.qll
+++ b/java/ql/lib/semmle/code/java/Expr.qll
@@ -7,6 +7,7 @@ module;
 import java
 private import semmle.code.java.frameworks.android.Compose
 private import semmle.code.java.Constants
+private import semmle.code.java.Overlay
 
 /** A common super-class that represents all kinds of expressions. */
 class Expr extends ExprParent, @expr {
@@ -2701,3 +2702,15 @@ class RecordPatternExpr extends Expr, @recordpatternexpr {
     )
   }
 }
+
+overlay[local]
+private predicate discardableExpr(string file, @expr e) {
+  not isOverlay() and
+  file = getRawFile(e)
+}
+
+/** Discard base expressions in files fully extracted in the overlay. */
+overlay[discard_entity]
+private predicate discardExpr(@expr e) {
+  exists(string file | discardableExpr(file, e) and extractedInOverlay(file))
+}
diff --git a/java/ql/lib/semmle/code/java/Javadoc.qll b/java/ql/lib/semmle/code/java/Javadoc.qll
index ef8f77bf9baf..101bab2723e0 100644
--- a/java/ql/lib/semmle/code/java/Javadoc.qll
+++ b/java/ql/lib/semmle/code/java/Javadoc.qll
@@ -5,6 +5,7 @@ overlay[local?]
 module;
 
 import semmle.code.Location
+private import semmle.code.java.Overlay
 
 /** A Javadoc parent is an element whose child can be some Javadoc documentation. */
 class JavadocParent extends @javadocParent, Top {
@@ -196,3 +197,15 @@ class KtCommentSection extends @ktcommentsection {
   /** Gets the string representation of this section. */
   string toString() { result = this.getContent() }
 }
+
+overlay[local]
+private predicate discardableJavadoc(string file, @javadoc d) {
+  not isOverlay() and
+  exists(@member m | file = getRawFile(m) and hasJavadoc(m, d))
+}
+
+/** Discard javadoc entities in files fully extracted in the overlay. */
+overlay[discard_entity]
+private predicate discardJavadoc(@javadoc d) {
+  exists(string file | discardableJavadoc(file, d) and extractedInOverlay(file))
+}
diff --git a/java/ql/lib/semmle/code/java/Member.qll b/java/ql/lib/semmle/code/java/Member.qll
index 662eab06bd1e..805ab0bf9402 100644
--- a/java/ql/lib/semmle/code/java/Member.qll
+++ b/java/ql/lib/semmle/code/java/Member.qll
@@ -11,6 +11,7 @@ import Annotation
 import Exception
 import metrics.MetricField
 private import dispatch.VirtualDispatch
+private import semmle.code.java.Overlay
 
 /**
  * A common abstraction for type member declarations,
@@ -623,7 +624,13 @@ class SrcMethod extends Method {
       then implementsInterfaceMethod(result, this)
       else result.getASourceOverriddenMethod*() = this
     ) and
-    (exists(result.getBody()) or result.hasModifier("native"))
+    (
+      // We allow empty method bodies for the local overlay variant to allow
+      // calls to methods only fully extracted in base.
+      isOverlay() or
+      exists(result.getBody()) or
+      result.hasModifier("native")
+    )
   }
 }
 
@@ -897,3 +904,33 @@ class ExtensionMethod extends Method {
     else result = 0
   }
 }
+
+overlay[local]
+private predicate discardableMethod(string file, @method m) {
+  not isOverlay() and
+  file = getRawFile(m) and
+  exists(@classorinterface c | methods(m, _, _, _, c, _) and isAnonymClass(c, _))
+}
+
+/** Discard base methods on anonymous classes in files fully extracted in the overlay. */
+overlay[discard_entity]
+private predicate discardAnonMethod(@method m) {
+  exists(string file | discardableMethod(file, m) and extractedInOverlay(file))
+}
+
+overlay[local]
+private predicate discardableBaseMethod(string file, @method m) {
+  not isOverlay() and
+  file = getRawFile(m)
+}
+
+overlay[local]
+private predicate usedOverlayMethod(@method m) { isOverlay() and methods(m, _, _, _, _, _) }
+
+/** Discard base methods in files fully extracted in the overlay that were not extracted in the overlay. */
+overlay[discard_entity]
+private predicate discardMethod(@method m) {
+  exists(string file |
+    discardableBaseMethod(file, m) and extractedInOverlay(file) and not usedOverlayMethod(m)
+  )
+}
diff --git a/java/ql/lib/semmle/code/java/Overlay.qll b/java/ql/lib/semmle/code/java/Overlay.qll
new file mode 100644
index 000000000000..713bd9f7623d
--- /dev/null
+++ b/java/ql/lib/semmle/code/java/Overlay.qll
@@ -0,0 +1,39 @@
+overlay[local?]
+module;
+
+import java
+
+/**
+ * A local predicate that always holds for the overlay variant and
+ * never holds for the base variant. This is used to define local
+ * predicates that behave differently for the base and overlay variant.
+ */
+overlay[local]
+predicate isOverlay() { databaseMetadata("isOverlay", "true") }
+
+/** Gets the raw file for a locatable. */
+overlay[local]
+string getRawFile(@locatable el) {
+  exists(@location loc, @file file |
+    hasLocation(el, loc) and
+    locations_default(loc, file, _, _, _, _) and
+    files(file, result)
+  )
+}
+
+/** Gets the raw file for a location. */
+overlay[local]
+string getRawFileForLoc(@location l) {
+  exists(@file f | locations_default(l, f, _, _, _, _) and files(f, result))
+}
+
+/** Holds for files fully extracted in the overlay. */
+overlay[local]
+predicate extractedInOverlay(string file) {
+  isOverlay() and
+  // The incremental Java extractor extracts skeletons without method
+  // bodies for dependencies. To approximate fully extracted files in
+  // the overlay, we restrict attention to files that contain an expression
+  // with an enclosing callable.
+  exists(@expr e | callableEnclosingExpr(e, _) and file = getRawFile(e))
+}
diff --git a/java/ql/lib/semmle/code/java/Statement.qll b/java/ql/lib/semmle/code/java/Statement.qll
index 73b0aac5cbdd..d1e7e748bc35 100644
--- a/java/ql/lib/semmle/code/java/Statement.qll
+++ b/java/ql/lib/semmle/code/java/Statement.qll
@@ -6,6 +6,7 @@ module;
 
 import Expr
 import metrics.MetricStmt
+private import semmle.code.java.Overlay
 
 /** A common super-class of all statements. */
 class Stmt extends StmtParent, ExprParent, @stmt {
@@ -987,3 +988,15 @@ class SuperConstructorInvocationStmt extends Stmt, ConstructorCall, @superconstr
 
   override string getAPrimaryQlClass() { result = "SuperConstructorInvocationStmt" }
 }
+
+overlay[local]
+private predicate discardableStmt(string file, @stmt s) {
+  not isOverlay() and
+  file = getRawFile(s)
+}
+
+/** Discard base statements in files fully extracted in the overlay. */
+overlay[discard_entity]
+private predicate discardStmt(@stmt s) {
+  exists(string file | discardableStmt(file, s) and extractedInOverlay(file))
+}
diff --git a/java/ql/lib/semmle/code/java/Variable.qll b/java/ql/lib/semmle/code/java/Variable.qll
index 50fd7a064846..9b8b42b71fba 100644
--- a/java/ql/lib/semmle/code/java/Variable.qll
+++ b/java/ql/lib/semmle/code/java/Variable.qll
@@ -5,6 +5,7 @@ overlay[local?]
 module;
 
 import Element
+private import semmle.code.java.Overlay
 
 /** A variable is a field, a local variable or a parameter. */
 class Variable extends @variable, Annotatable, Element, Modifiable {
@@ -133,3 +134,15 @@ class Parameter extends Element, @param, LocalScopeVariable {
   /** Holds if this is an anonymous parameter, `_` */
   predicate isAnonymous() { this.getName() = "" }
 }
+
+overlay[local]
+private predicate discardableLocalVarDecl(string file, @localscopevariable l) {
+  not isOverlay() and
+  file = getRawFile(l)
+}
+
+/** Discard base local scoped variables in files fully extracted in the overlay. */
+overlay[discard_entity]
+private predicate discardLocalVarDecl(@localscopevariable l) {
+  exists(string file | discardableLocalVarDecl(file, l) and extractedInOverlay(file))
+}
diff --git a/java/ql/src/experimental/Security/CWE/CWE-020/Log4jJndiInjection.ql b/java/ql/src/experimental/Security/CWE/CWE-020/Log4jJndiInjection.ql
index 84c4bb01c126..3abaa7bdcfa3 100644
--- a/java/ql/src/experimental/Security/CWE/CWE-020/Log4jJndiInjection.ql
+++ b/java/ql/src/experimental/Security/CWE/CWE-020/Log4jJndiInjection.ql
@@ -22,6 +22,7 @@ import semmle.code.java.dataflow.ExternalFlow
 private import semmle.code.java.security.Sanitizers
 import Log4jInjectionFlow::PathGraph
 
+overlay[local?]
 deprecated private class ActivateModels extends ActiveExperimentalModels {
   ActivateModels() { this = "log4j-injection" }
 }
diff --git a/java/ql/src/experimental/Security/CWE/CWE-036/OpenStream.ql b/java/ql/src/experimental/Security/CWE/CWE-036/OpenStream.ql
index c84037719da9..0929ca3eb805 100644
--- a/java/ql/src/experimental/Security/CWE/CWE-036/OpenStream.ql
+++ b/java/ql/src/experimental/Security/CWE/CWE-036/OpenStream.ql
@@ -17,6 +17,7 @@ import semmle.code.java.dataflow.FlowSources
 import semmle.code.java.dataflow.ExternalFlow
 import RemoteUrlToOpenStreamFlow::PathGraph
 
+overlay[local?]
 deprecated private class ActivateModels extends ActiveExperimentalModels {
   ActivateModels() { this = "openstream-called-on-tainted-url" }
 }
diff --git a/java/ql/src/experimental/Security/CWE/CWE-073/FilePathInjection.ql b/java/ql/src/experimental/Security/CWE/CWE-073/FilePathInjection.ql
index c87097458520..11bb600ffe85 100644
--- a/java/ql/src/experimental/Security/CWE/CWE-073/FilePathInjection.ql
+++ b/java/ql/src/experimental/Security/CWE/CWE-073/FilePathInjection.ql
@@ -22,6 +22,7 @@ import semmle.code.java.security.PathSanitizer
 private import semmle.code.java.security.Sanitizers
 import InjectFilePathFlow::PathGraph
 
+overlay[local?]
 deprecated private class ActivateModels extends ActiveExperimentalModels {
   ActivateModels() { this = "file-path-injection" }
 }
diff --git a/java/ql/src/experimental/Security/CWE/CWE-078/ExecTainted.ql b/java/ql/src/experimental/Security/CWE/CWE-078/ExecTainted.ql
index 08f7631af828..c13bc3bb245c 100644
--- a/java/ql/src/experimental/Security/CWE/CWE-078/ExecTainted.ql
+++ b/java/ql/src/experimental/Security/CWE/CWE-078/ExecTainted.ql
@@ -18,6 +18,7 @@ import semmle.code.java.security.CommandLineQuery
 import InputToArgumentToExecFlow::PathGraph
 private import semmle.code.java.dataflow.ExternalFlow
 
+overlay[local?]
 deprecated private class ActivateModels extends ActiveExperimentalModels {
   ActivateModels() { this = "jsch-os-injection" }
 }
diff --git a/java/ql/src/experimental/Security/CWE/CWE-200/AndroidWebResourceResponse.qll b/java/ql/src/experimental/Security/CWE/CWE-200/AndroidWebResourceResponse.qll
index bd898df205a8..b988398e4c26 100644
--- a/java/ql/src/experimental/Security/CWE/CWE-200/AndroidWebResourceResponse.qll
+++ b/java/ql/src/experimental/Security/CWE/CWE-200/AndroidWebResourceResponse.qll
@@ -7,6 +7,7 @@ private import semmle.code.java.dataflow.ExternalFlow
 private import semmle.code.java.dataflow.FlowSteps
 private import semmle.code.java.frameworks.android.WebView
 
+overlay[local?]
 private class ActivateModels extends ActiveExperimentalModels {
   ActivateModels() { this = "android-web-resource-response" }
 }
diff --git a/java/ql/src/experimental/Security/CWE/CWE-400/ThreadResourceAbuse.qll b/java/ql/src/experimental/Security/CWE/CWE-400/ThreadResourceAbuse.qll
index ce6de1a06798..12ba6769f742 100644
--- a/java/ql/src/experimental/Security/CWE/CWE-400/ThreadResourceAbuse.qll
+++ b/java/ql/src/experimental/Security/CWE/CWE-400/ThreadResourceAbuse.qll
@@ -8,6 +8,7 @@ import semmle.code.java.arithmetic.Overflow
 import semmle.code.java.dataflow.FlowSteps
 import semmle.code.java.controlflow.Guards
 
+overlay[local?]
 private class ActivateModels extends ActiveExperimentalModels {
   ActivateModels() { this = "thread-resource-abuse" }
 }
diff --git a/java/ql/src/experimental/Security/CWE/CWE-625/PermissiveDotRegexQuery.qll b/java/ql/src/experimental/Security/CWE/CWE-625/PermissiveDotRegexQuery.qll
index 8fe997793f4a..f8e328902504 100644
--- a/java/ql/src/experimental/Security/CWE/CWE-625/PermissiveDotRegexQuery.qll
+++ b/java/ql/src/experimental/Security/CWE/CWE-625/PermissiveDotRegexQuery.qll
@@ -9,6 +9,7 @@ import semmle.code.java.controlflow.Guards
 import semmle.code.java.security.UrlRedirect
 import Regex
 
+overlay[local?]
 private class ActivateModels extends ActiveExperimentalModels {
   ActivateModels() { this = "permissive-dot-regex-query" }
 }
diff --git a/shared/dataflow/codeql/dataflow/internal/DataFlowImplCommon.qll b/shared/dataflow/codeql/dataflow/internal/DataFlowImplCommon.qll
index 5cb92d7ba8da..288814c4c511 100644
--- a/shared/dataflow/codeql/dataflow/internal/DataFlowImplCommon.qll
+++ b/shared/dataflow/codeql/dataflow/internal/DataFlowImplCommon.qll
@@ -291,6 +291,7 @@ module MakeImplCommon<LocationSig Location, InputSig<Location> Lang> {
      * to `lambdaCall`, if any. That is, `lastCall` is able to target the enclosing
      * callable of `lambdaCall`.
      */
+    overlay[global]
     pragma[nomagic]
     predicate revLambdaFlow(
       Call lambdaCall, LambdaCallKind kind, Node node, Type t, boolean toReturn, boolean toJump,