This might be helpful.
https://www.nullskull.com/articles/20031103.asp
I'm not exactly sure what you are after here. That said, it is important to note that C# does not support multiple inheritance of "classes" but it does support implementing multiple interfaces.
I "think" you might be trying to stuff too much into one "interface" of sorts then getting frustrated when one of your higher level classes doesn't need a method or property. You "may" want to consider small interfaces and only implementing those Interfaces that are needed on a given class. This would let you pass around the based functionality of a class as well as create methods that accept a limited Interface and still pass the same class through as a parameter.