@gnarley_boot @Tactical @trumpgpt @realman543 I strongly recommend Spirit Island.
Jagged Earth adds support for 5-6 players (base game is 1-4). Operation Flashpoint is probably my second-favourite co-op game and it's a bit too simple for good co-op. Although I have only played Zombicide once or twice, I should get that maybe.
Also highly recommend Tragedy Looper for 4p specifically; it can work with 2 or 3 but it's not as good. Also you have to be careful about not looking at the mastermind cards... Until you get into writing your own scripts. Pity that tragedylooperscripts.com is gone.
Wingspan is good for a while but kinda gets boring. I haven't tried 6-7p mode added in Asia expansion, because I got Earth shortly after which I think solves the problem much more elegantly.
Terraforming Mars has a decent amount of replayability too, and it's fun engine-building shenanigans.

In the line of chess I recommend Sirlin's Chess 2. Truthfully, I haven't played it, but "memorising openings is boring, let's have 36 possible opening matchups" and "chasing an obviously losing player's king around the board is boring, let's just have you win if you get your king on his side" are both pretty good opinions.

More of Sirlin (who also made an excellent fighting game, but that's irrelevant to this topic)...
Puzzle Strike is basically peak deckbuilder. Puzzle Strike 2 was a bit of a letdown by comparison, but still decent enough.
Yomi... I didn't like much when I played it. Now that I understand fighting games maybe I will like it. Sirlin insists that it's good even for people who know nothing of fighting games but I'm not sure I believe it.
Pandante is an actual game based on Texas Hold 'Em, and I am absolute dogshit at it.
Probably all of these are hard to come by, you may have to buy second-hand or print your own, good luck figuring out where the pnp assets are squirrelled away... I think on sirlingames.com.

Anyway, Spirit Island. Cannot recommend enough. Fucking amazing game.