Interfaces: re-use implementations?

I am wondering if there’s a way to re-use interface implementations in multiple classes that can’t have a common base-class implementing the interface but do share a base-class that the interface could treat them as (like AActor).

I want to customize the way that actors respond to a large number of different input-events without making the interface itself too specific, more like OnLeftButtonDown, Up etc.

If it’s not possible I will probably implement additional interfaces that get used by the “InputReceiving” interface across similar classes. Or I will just stuff everything into one, even if most users won’t be needing most of it. But maybe there’s a way to derive an interface from a base interface? Or some other way to call a specific function implementation?..