Try using "4 adults" in your search on Hilton, Hyatt, Marriott. You may still get some non-Suites but for the most part a 4 adult stay requires some sort of suite at a minimum which should make it easier to navigate and find multi-room suites.

I think these are pretty infrequent in non-resort hotels or require you to book the top suite in a given chain.

It may be cheaper (and easier) to just book 2 adjoining hotel rooms (that's what my parents did when I was growing up).