Remember that the Job system only really limits the PC because they're using Soul Crystals to basically cheat their way into skill.

With enough training and/or talent it'd be entirely plausible to transcend the Job system. Without spoiling too much Thancred later changes to a Gunbreaker, but retains some stealth tricks he employs during a climactic confrontation with Shadowbringers' secondary antagonist. Of course, animations limit every Job, and given Jobs are all animated with a specific weapon in mind...