The four-player picks, and their honest limits
Diablo IV is the standout for a pair who want something long. Two players share the screen on console - unusual for a modern live-service RPG - and the same save works online with friends on Xbox and PC afterwards, because it has full crossplay and cross-progression. It is a seasonal game, so it rewards a group that plays regularly rather than once. Full detail in the Diablo IV review.
Borderlands 3 is the four-player looter, and the better buy if you want a campaign with an ending and no seasons to keep up with. Split-screen on console is a headline feature. The catch is that it has no crossplay at all, so everyone playing online with you has to be on PlayStation - see the Diablo IV vs Borderlands 3 comparison for which of the two your group should actually own.
Sackboy: A Big Adventure is the gentle option, and the one to reach for when the second player is a child or a total newcomer. Teams of two to four take on levels together, locally or online, and the tone stays friendly right up until a couple of late co-op stages that will make two adults argue. It is PlayStation and PC only with no crossplay listed, so treat online as same-platform.
Overcooked! All You Can Eat is the party pick and the only game here with full crossplay on top of local play - four people in the room, or four people on four different systems, or any mix. LEGO Star Wars and Rayman Legends are the all-ages couch options, and Human: Fall Flat is the one that costs less than lunch and scales to eight online.
When the answer is honestly a different console
If your room regularly holds four people who all want a controller, PS5 is not the best tool for the job and we would rather say so. Nintendo builds four-player local multiplayer into almost everything it publishes, and the Switch page reflects that. Xbox has the deepest split-screen back catalog of the three, including Minecraft's four-player split-screen, which the PS5 edition also supports but which Xbox players get through Game Pass - the Xbox split-screen list goes into it.
For a pair, though, PS5 wins outright, because the two best split-screen games ever made are both on it and both let the second person play without buying anything.
Taking a split-screen game online
Several picks here do something more interesting than either format alone: they let two people on one couch join an online session with friends elsewhere, so you get four players from two consoles. Borderlands 3, Diablo IV and Minecraft all support it. That specific trick has its own page - split-screen games you can also play online - because it is the single most under-used feature in group gaming and almost nobody knows which games have it.
If everyone is in a different house, start at the PS5 and PC crossplay page or the wider two-player list instead, and treat split-screen as a bonus rather than the plan.
Two specific titles generate more questions than the rest of the PS5 list combined. Call of Duty's split-screen is two players, PS5 and Series X|S only, and needs both a connection and a subscription - the rules are quoted from Activision at how to play split-screen on Black Ops 7. Fortnite's is also two players and requires player two to have their own Epic account, covered at Fortnite split-screen.
Two more PS5 questions have their own pages now. If you want a racing game to divide the screen, the cap is the whole decision - four for the kart racers, two for Gran Turismo 7 - and the per-game numbers are at best split-screen racing games. And Borderlands 4, the newest big-budget shooter on the PS5 that still splits, is two players rather than four, with an unusual trick where two local pairs can join into one online party: our Borderlands 4 reviewhas the rules quoted from 2K's own FAQ.