It would not be hard to create an all-warlock version of the "iconic 4."
Fighter: Hexblade Pact of the Blade with the Thirsting Blade and Lifedrinker invocations.
Wizard/Evoker: Fiend Pact of the Tome with the Book of Ancient Secrets and Agonizing Blast invocations.
Cleric: Celestial Pact of the Chain/Tome with the Agonizing Blast invocation.
Rogue: Fey Pact of the Chain/Tome with the criminal or urchin background.
Yeah, the DM and players would have to come up with some reason why the group was working together, especially the Fiend and Celestial warlocks. One idea I had was to play on the tensions between true deities and the entities who create warlock pacts. Perhaps all the gods decide warlock pacts are a threat to their power (clerics are the only true way!) and set out to eradicate them. The warlock patrons are forced to band together out of self-interest.
Or maybe the fiend and celestial patrons are actually the same patron. It is a powerful trickster entity playing both sides, lol.
Maybe it's a loophole thing, Asmodeus and some other gods need to do something but can't interfere directly in the situation due to some sort of divine treaty so they reach out to the patrons and have them put a team together. Maybe to stop one of the other god from doing something they shouldn't?