Yes but they would clip through half your body almost all the time. Hrogthar and Viera would clip extra bad.
I'd rather have one class invented by the player character, like going from summoner to exclusively using permanent trances as stances as the class mechanic. Could be a Ranged/magic/melee DPS where Ifrit is melee, Garuda is ranged and Ramuh is magic, or something like that.
With all the options, it could conceivably be a class that is anything and everything at the same time, with different kits based on trance so you'd only need one new job for an expansion since it could fulfil all aspects of the trinity. Too bad SE doesn't support thinking on company time, so put some nostalgia bait in instead and rake in the cash.
Anyway, i'm gonna call it now: the next job uses a whip, swordwhip or both.