If you really want this idiomatically correct, put the data in JSON or other suitable format, zip it and encode in Base64 to pass via GET as a single parameter. To hit the browser limits you will need so big query that you may hit UX constraints earlier in many cases (2048 bytes is 50+ UUIDs or 100+ polygon points etc).

Pros: the search query is a link that can be shared, the result can be cached. Cons: harder to debug, may not work in some cases due to URI length limits.