Didn't Lisp solve this problem in the 1980's with generic functions and multiple dispatch? I'm referring to the Common Lisp Object System (CLOS), and its predecessors, New Flavors and CommonLoops. I see no mention of this prior art in the paper.

CLOS is an object-oriented system, which solves the problem of adding new functions without modifying existing class definitions, by placing generic functions outside of class definitions.

A group of generic functions comprise a protocol of some kind. Sometimes you cannot extend in the way you need without changing the protocol.