We prefer same/shared screen co-op (Diablo 3 and 4, A Way Out, etc.), and story campaign PvE co-op (e.g. Wildlands, BG3).
Shared screen co-op is annoyingly difficult to find since "couch co-op" doesn't differentiate split screen versus shared screen and we strongly dislike split screen.
Story co-op is increasingly difficult to find. When you do find them, they tend to be less campaign or story and more "repeated encounter" scenarios (e.g., Insurgent). There is nothing like the strategically deliberate plan and work together pace of Wildlands since Wildlands.
Worse, recent co-op campaign games tend to be add-on modes to PvP, meaning you have to contend with ridiculous "balance" boosts and nerfs so nothing works like it should if it was a single player game. PvE should not be "balanced" this way.
If you didn't already try "It Takes Two" then you owe it to yourselves to try, although I don't know off the top of my head if it's playable as shared-screen.
It definitely ticks the "co-op story" game box though, and is overall a great game.
Like for Pikmin where in the later editions there were multiple main characters on the field that you could switch between. How was there not a local co-op where each player could use a main character?
If you liked BG3, have you tried the Divinity Original Sin series by the same studio? They're even better in co-op IMO and not being limited to the D&D rules makes combat more fun and dynamic.
Shared screen co-op is annoyingly difficult to find since "couch co-op" doesn't differentiate split screen versus shared screen and we strongly dislike split screen.
Story co-op is increasingly difficult to find. When you do find them, they tend to be less campaign or story and more "repeated encounter" scenarios (e.g., Insurgent). There is nothing like the strategically deliberate plan and work together pace of Wildlands since Wildlands.
Worse, recent co-op campaign games tend to be add-on modes to PvP, meaning you have to contend with ridiculous "balance" boosts and nerfs so nothing works like it should if it was a single player game. PvE should not be "balanced" this way.