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I was familiar with the problem but didn't have a name for it; thanks for providing me with one. What kind of work has there been on creating programming paradigms that make it easy to both add new types and new methods? Is it a CAP-theorem-type problem where every solution is a trade-off, or is there a way to have your cake and eat it too?
There are languages (libraries) that solve it. For reference, check Clojure's multimethods and OCaml's polymorphic variants.
For example, if I'm writing a normal Java class, I know where I go to find methods dealing specifically with instances Foo (namely Foo and its children and direct users); with multimethods, it's more likely that there is some multimethod out there in an unrelated class that looks for instances of Foo.