Is the idea limited to XIV summons? There are several that haven't appeared outside of other games that would probably gel well with XIV's jobs. Hecatoncheir hasn't appeared as a summon outside of 13, but considering what his inscription is, he'd fit monks extremely well.

By the grace of Etro, arise great and mighty giant. Come forth, thee who shoulders the sky.
A name in blood, a pact of strength. Hecatoncheir shall rise, his bond eternal and unyielding.
Hands that purge impurity. Arms that harbor strength.