Mirror Universe

Alternate reality, where alternate versions of the main characters exist. Through some bizarre circumstance, they cross over to the normal universe, or the normal characters cross over to the alternate one.

Sometimes the alternate characters are evil twins (Justice Lords), other times they're just alternate selves (Fullmetal Alchemist).

In D&D, this has many possibilities. The easiest would be having the evil twins be enemies, or even just having one party member's evil twin be an opponent (especially a smart one who "knows how they think.")

Another option would be a temporary team-up, where they work with their alternate selves to avoid some major catastrophe that affects both realities. Or for a twist, to fight their evil twins, they have to work with the GOOD twins of their regular enemies. (IE, Justice League working with alternate reality good Luthor, to fight the Justice Lords.) You could take this even further by having the team-up members be a mix of real and alternate selves, but that might be too confusing.

Another option that would be less encounter-based would be meeting their alternate selves, who are fundamentally the same except for a major, major difference which isn't learned until after teaming up with them for a while. Maybe they're willing to execute in cold blood, or intensely religious, or even VAMPIRES (or werewolves.) But important to note that despite these differences, they are not dealbreaking, ie the party reaction should be one of shock and "what do we do now?" and not "They're monsters, kill them!"

Finally, another option that simplifies things by eliminating the need for two groups is having the party end up in their alternate selves' bodies. (Maybe the alternates end up in THEIR bodies, but maybe their minds just disappear for awhile.) Party has to deal with strange world, strange friends, and unknown EVERYTHING. Makes for an interesting mini-adventure. Sample: JLA ending up in alternate bodies in Rock of Ages storyline.