diff --git a/extensions/arc/deployment/src/main/java/io/quarkus/arc/deployment/AutoAddScopeBuildItem.java b/extensions/arc/deployment/src/main/java/io/quarkus/arc/deployment/AutoAddScopeBuildItem.java
index 805ef0aab7000..3de2e134b35ad 100644
--- a/extensions/arc/deployment/src/main/java/io/quarkus/arc/deployment/AutoAddScopeBuildItem.java
+++ b/extensions/arc/deployment/src/main/java/io/quarkus/arc/deployment/AutoAddScopeBuildItem.java
@@ -77,7 +77,7 @@ public interface MatchPredicate {
 
         /**
          * @param clazz
-         * @param annotations
+         * @param annotations The current set of (possibly transformed) annotations
          * @param index
          * @return {@code true} if the input arguments match the predicate,
          *         {@code false} otherwise
@@ -85,10 +85,11 @@ public interface MatchPredicate {
         boolean test(ClassInfo clazz, Collection<AnnotationInstance> annotations, IndexView index);
 
         default MatchPredicate and(MatchPredicate other) {
+            MatchPredicate previous = this;
             return new MatchPredicate() {
                 @Override
                 public boolean test(ClassInfo clazz, Collection<AnnotationInstance> annotations, IndexView index) {
-                    return test(clazz, annotations, index) && other.test(clazz, annotations, index);
+                    return previous.test(clazz, annotations, index) && other.test(clazz, annotations, index);
                 }
             };
         }
@@ -140,6 +141,8 @@ public Builder unremovable() {
 
         /**
          * Set a custom predicate.
+         * <p>
+         * The previous predicate (if any) is replaced.
          *
          * @param predicate
          * @return self
@@ -286,7 +289,13 @@ public Builder scopeAlreadyAdded(BiConsumer<DotName, String> consumer) {
             return this;
         }
 
-        private Builder and(MatchPredicate other) {
+        /**
+         * The final predicate is a short-circuiting logical AND of the previous predicate (if any) and this condition.
+         *
+         * @param other
+         * @return self
+         */
+        public Builder and(MatchPredicate other) {
             if (matchPredicate == null) {
                 matchPredicate = other;
             } else {
diff --git a/extensions/arc/deployment/src/test/java/io/quarkus/arc/test/autoscope/AutoScopeBuildItemTest.java b/extensions/arc/deployment/src/test/java/io/quarkus/arc/test/autoscope/AutoScopeBuildItemTest.java
index 9212a428a2224..bf42fdc62815b 100644
--- a/extensions/arc/deployment/src/test/java/io/quarkus/arc/test/autoscope/AutoScopeBuildItemTest.java
+++ b/extensions/arc/deployment/src/test/java/io/quarkus/arc/test/autoscope/AutoScopeBuildItemTest.java
@@ -9,7 +9,9 @@
 import jakarta.annotation.PostConstruct;
 import jakarta.enterprise.inject.Instance;
 import jakarta.inject.Inject;
+import jakarta.inject.Named;
 
+import org.jboss.jandex.DotName;
 import org.jboss.logging.Logger;
 import org.junit.jupiter.api.Test;
 import org.junit.jupiter.api.extension.RegisterExtension;
@@ -31,9 +33,11 @@ public class AutoScopeBuildItemTest {
                 b.addBuildStep(new BuildStep() {
                     @Override
                     public void execute(BuildContext context) {
-                        context.produce(AutoAddScopeBuildItem.builder().match((clazz, annotations, index) -> {
-                            return clazz.name().toString().equals(SimpleBean.class.getName());
-                        }).defaultScope(BuiltinScope.DEPENDENT)
+                        context.produce(AutoAddScopeBuildItem.builder()
+                                .match((clazz, annotations, index) -> {
+                                    return clazz.name().toString().equals(SimpleBean.class.getName());
+                                })
+                                .defaultScope(BuiltinScope.DEPENDENT)
                                 .scopeAlreadyAdded((scope, reason) -> {
                                     // We can't pass the state directly to AutoScopeBuildItemTest because it's loaded by a different classloader
                                     Logger.getLogger("AutoScopeBuildItemTest").info(scope + ":" + reason);
@@ -43,17 +47,30 @@ public void execute(BuildContext context) {
                 b.addBuildStep(new BuildStep() {
                     @Override
                     public void execute(BuildContext context) {
-                        context.produce(AutoAddScopeBuildItem.builder().match((clazz, annotations, index) -> {
-                            return clazz.name().toString().equals(SimpleBean.class.getName());
-                        }).defaultScope(BuiltinScope.SINGLETON).priority(10).reason("Foo!").build());
+                        context.produce(AutoAddScopeBuildItem.builder()
+                                .match((clazz, annotations, index) -> {
+                                    return clazz.name().toString().equals(SimpleBean.class.getName());
+                                })
+                                .anyMethodMatches(m -> m.hasAnnotation(PostConstruct.class))
+                                .isAnnotatedWith(DotName.createSimple(Named.class))
+                                .defaultScope(BuiltinScope.SINGLETON)
+                                .priority(10)
+                                .reason("Foo!")
+                                .build());
                     }
                 }).produces(AutoAddScopeBuildItem.class).build();
                 b.addBuildStep(new BuildStep() {
                     @Override
                     public void execute(BuildContext context) {
-                        context.produce(AutoAddScopeBuildItem.builder().match((clazz, annotations, index) -> {
-                            return clazz.name().toString().equals(NotABean.class.getName());
-                        }).defaultScope(BuiltinScope.SINGLETON).unremovable().build());
+                        context.produce(AutoAddScopeBuildItem.builder()
+                                .match((clazz, annotations, index) -> {
+                                    return clazz.name().toString().equals(NotABean.class.getName());
+                                })
+                                .containsAnnotations(DotName.createSimple(PostConstruct.class))
+                                .and((clazz, annotations, index) -> annotations.isEmpty())
+                                .defaultScope(BuiltinScope.SINGLETON)
+                                .unremovable()
+                                .build());
                     }
                 }).produces(AutoAddScopeBuildItem.class).build();
             }).setLogRecordPredicate(log -> "AutoScopeBuildItemTest".equals(log.getLoggerName()))
@@ -76,6 +93,7 @@ public void testBeans() {
         assertEquals(notABean1.ping(), Arc.container().instance(NotABean.class).get().ping());
     }
 
+    @Named
     static class SimpleBean {
 
         private String id;