Sort of, but probably not in the way you're thinking. You can write multiple dependent claims (although they are generally disfavored in the U.S. and cost extra in fees). But say you have something like this:
What is claimed is:
1. A chair comprising a seat and a plurality of legs.
2. The chair of claim 1, wherein said plurality of legs comprises four legs.
3. The chair of any preceding claim, wherein said seat is made of plastic.
So claim 3 is a multiple dependent claim, but the way it would be interpreted is basically as having the scope as if it were written as two separate claims: one depending from claim 1 (thus covering any chair with a plastic seat and some legs), and one depending from claim 2 (thus covering any chair with a plastic seat and four legs). So it's just a concise way of writing something that would logically expand into more than one claim, which isn't really the same thing as multiple inheritance in programming.
