If your API could benefit from a particular verb (SEARCH, MOVE, CHECKOUT), just use it. You don't need (more) permission from (another) RFC - RFC 2616 and 7231 [1] already gave you permission to add verbs.
Most libraries and tools support arbitrary verbs including `XMLHttpRequest` and `curl`. Yes, there are a few libraries and frameworks that don't easily support arbitrary verbs, but the ones that have added support for PATCH generally have opened up.
Look, there are two Internets. One for people and one for machines. Our RESTful APIs are intended for consumption by machines, not people. You don't have to wedge everything into GET and POST and abuse query parameters to convey what you really mean.