Is it possible to extend Spring @RequestMapping with an own annotation?

I have a custome annotation:

@Target({ElementType.TYPE})
@Retention(RetentionPolicy.RUNTIME)
@Controller
@RequestMapping("auth/firebase")
public @interface FirebaseAuth {
    @AliasFor(annotation = RequestMapping.class, attribute = "path")
    String[] path() default {};
}

I want to achive, that a controller which is annotated with:

@FirebaseAuth(path = "user")
public class UserController {

Will end up with a path like this: auth/firebase/user, to secure the resource

How is it possible to extend the path with auth/firebase before "user" with an annotation (not with a superclass)?

Thanks! :)