4-Player Story Mode in Super Smash Bros.? No, But Co-op Options Exist

No Super Smash Bros. game has a 4-player co-op story mode.

• Subspace Emissary (Brawl): 1–2 Player Co-op (Player 2 joins anytime).
• World of Light (Ultimate): Single Player only (Spirits mode).
• Classic / Adventure Modes: 1 Player.

4-Player Co-op Options in Smash

• Smash (Versus): 2v2 Team Battle (4 players, 2 teams).
• Squad Strike (Ultimate): 3v3 or 5v5 Tag Team (local/online).
• Stage Builder / Shared Content: Play custom stages together.
• Spirit Board (Ultimate): 1 Player (can't co-op).

Games With 4P Co-op Story / Campaign

• Kirby's Return to Dream Land / Forgotten Land / Star-Crossed World (4P drop-in).
• New Super Mario Bros. U / Wii (4P).
• Rayman Legends (4P).
• Minecraft Dungeons (4P).
• Diablo III (Console) (4P local).
• Borderlands 2/3 (PC Nucleus Co-op) (4P local).

Smash is a party fighter, not a co-op adventure.