While the "Invincible" set is the only one with a gameplay-altering perk, you can find other cosmetic sets to change Jesse's appearance:
: Once unlocked, the armor set becomes available for use on all other current or future save files , including standard runs where permadeath is not active. Other "Sets" and Customization Evil West on sets
: You must finish the entire game on the Through Death (permadeath) setting. While the "Invincible" set is the only one