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Promethean is the only one that gives you a massable lategame melee unit, the Phoenix Walker. It also has some supporting mods for melee units, like backlash projectors (whenever this unit is hit, it deals 12 thermal damage to all adjacent enemies; +2 armour). The Plasmoid is a cheap strategic summon that has a melee attack, flanking immunity and an innate weaker version of backlash (which stacks with the mod).

Voidtech is a strong contender for early melee, with the Echo Walker and the Phase Modulator (pass through obstructions without penalty; +1 shield) which you can put on your other melee infantry. Voidtech is very ranged-focused lategame, though.

Celestian has a strong early game melee unit in the Lightbringer and has mods and operations to penalise enemies attacking it and keep it healed. The Amazon Lightbringer deserves special mention for being flying. Again, beyond that it's mostly ranged.

Xenoplague has a lot of options for getting up close. Plague pods are ranged, but best placed on units that don't mind getting stuck in melee due to its short range. The first two stages of the Xenoplague unit, the Pustule and Destroyer, are competent in melee before finally evolving into the more ranged/support Plague Lord.

Synthesis doesn't melee, but Total Network Integration is the best mod in the game regardless what your plans are.

Psynumbra is largely ranged, but the Echoes of Despair it can summon by killing units are melee attackers and can blow themselves up to inflict even more enemies with Despair. And once you get to the endgame, the Herald of Oblivion is the most powerful melee unit in the game.
 
Melee-focused units can't deal with fliers, so probably Psynumbra for Consuming Gaze so your melee pals can still mind-zap fliers out of the sky.