We have liftoff: local multiplayer Minecraft on the same Steam Deck.

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in Desktop mode, download PartyDeck 0.3.2, the PartyDeck config for Minecraft, the "Vertical split for 2 players" config, and the Prism Portable launcher (the flatpak will not work for this). If you want separate skins for p1 and p2, download those now.
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Extract PartyDeck and Prism to their own folders, like ~/Games/partydeck and ~/Games/prism.
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run PrismLauncher for the first time and log into your Minecraft account. Add two "offline" accounts, I named mine "red" and "blue".
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Create a new instance of 1.20.1 Fabric named Splitscreen Red with these mods:
- fabric api 0.86.1
- fabric tailor 2.1.2
- midnight controls 1.9.4
- splitscreen 0.0.2
- whoami 1.0
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Place your skins in the instance folder, for example mine are in minecraft/skins.
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Under Settings -> Miscellaneous, set Account to "red".
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Create a duplicate of that instance named Splitscreen Blue, and set its Account to "blue".
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Following the PartyDeck readme, set up a steam shortcut to PartyDeckKWinLaunch.sh.
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Launch PartyDeck, select Minecraft -> Play. You will be prompted to select the folder where you installed Prism Launcher earlier.
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Under PartyDeck settings, enable "Vertical split for 2 players".
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Reboot into Gaming Mode.
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Make sure you have connected two controllers and a mouse.
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Launch PartyDeck from Gaming Mode.
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Select Minecraft -> Play. Press "a" (or whatever the south button is) on both controllers, then press "start" on player 1's controller.
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This will start two copies of Prism. Using the mouse, launch the Red instance for player 1 and the Blue instance for player 2. Fullscreening both instances should Just Work, but if it doesn't, connect a keyboard and press F11 repeatedly to cycle through the different configs for the Splitscreen mod.
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Have player 1 start a singleplayer world, and open it to LAN.
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Have player 2 join via the multiplayer menu.
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Each player should now set their skin using this command:
/skin set upload <original|slim> skins/<skin.png>
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If the skins do not render correctly, have both players exit and re-launch the game.
At this point you should be good to go! You have two copies of minecraft running in splitscreen on one computer, with different names and avatars for each player, in the same world.
This took me like three days to figure out. If it helped you, please send me an email!
map shown here is Questioning by Infernally. skins are Panty and Stocking by Ayahanna.