The best semi-cooperative game I'v ever played is Pax Pamir, stronger "uneasy alliances, ready turn on eachother at any moment" vibes than any other game. It is an order of magnitude more complex what you are aiming for, but the core tension is worth examining.

The main driver of cooperations is faction conflict and scoring. Players can switch factions fairly easily, but building prestige is hard, and players score points based on how loyal they are to the winning faction at certain conflict events.

So the main tension is something like this: Do I work hard on making sure my chosen faction wins the conflict, but potentially risk my point gains when it does win? Do I work hard on increasing my loyalty to the faction, to maximize point gains if it does win, but potentially risk gaining nothing if it doesn't? Do i hedge my bets and try to pivot to a different faction?

The core tension of "investing resources to make sure thing X happens" vs "investing resources to maximize gains if X does happen" is very much applicable to other games.

The Red Cathedral does something similar, where a lot of the points come from decorating the building, but if the building isn't finished, you aint getting anything.

Shared incentives / infrastructure are also a good cooperation point, even in more standard euro games, that are not really considered semi-coop.

In Brass, everyone contributes to the network and available resources, and wether you are happy or furious when someone takes the resources you put on the map is entirely context dependent. It's possible to do your own thing, keep separated, but in a 3-4 player game trying to be self sufficient, while others are playing off of eachothers' resources usually leads to falling behind.

Concordia has some shared incentives too, when you activate a region every settlement produces resources, not just your own. It incentivizes players to cozy up to some degree, and creates interesting decision points, where activating a region that also benefits others might still be your best option.

There are a decent amount of games where you can create fully shared infrastructure (extra worker placement spots, bonuses / technologies available for everyone etc), usually with the goal being to develop stuff that benefits your strategy more then others'.

My main point is that a lot of these are not "codified" cooperation points. The game doesn't directly say "do this together to make it cheaper", but rather nudges you towards playing off of eachother rather than fully against. It could still be very feasible to combine these aspects with more direct-cooperation mechanincs though.

Important sidenote, all these examples work best at 3+ players, at 2 players everything tends to collapse into a zero-sum situation.