I’m using interface inheritance to enforce composition at the class level

And because my classes are parcelable, I allow the writeToParcel method in each interface to call its super to add its own members to the parcel

That’s one use case

So there isn’t really anything to disagree with.

But to help address your problem, I try to lean towards the Decorator pattern https://en.wikipedia.org/wiki/Decorator_pattern

Rather than forcing a child class method to ask it’s parent method to do work, you pass in a “CommonFoo” class instance to a “SpecificFoo” classes constructor, and allow the “SpecificFoo” class to add additional info to that method