I'm not a fan of the newXCOM class system, but I can live with it. It's rigid and arbitrary. Classic X-COM may have been a little bland, but I enjoyed the flexibility.
So here's an idea that should fit well with Phoenix Point mechanics I know so far.
Retraining to another class
The most obvious one, to adapt to new situation. Maybe your messed and two of your best frontline soldiers died. You have too many snipers now. You'd rather repurpose an experienced sniper than use rookies (this preference may differ from player to player). In new XCOM class system, I think you can't do that. In old X-COM, it was quite straightforward, you just changed their equipment. Their stats, trained at a different role, might not be optimal, but they would be more effective than a complete rookie. (When I played TFTD, I didn't understand all the mechanics so I equipped most people with Sonic Cannons. After a period of sweating and slowly creeping forward, most of my soldiers got used to carrying heavy loads and moved quite fast with the cannons! Still no 2 shots per turn though).
Less obvious - as a creative, thematic workaround to soldier traumas and afflictions. Your Assault guy had too many bullets whiz past his head and now has battle fright ? In new XCOM, no good solution. With ability to change classes, you could make him into a sniper so he can calm down a bit. Or maybe your sniper had a few fingers bitten off. He can no longer aim very well. What you're going to do - suffer a bad sniper, or send him away? What if you didn't have to? You could turn him into a technician, and his poor accuracy is no longer a big problem.
At the very least, it should be possible to turn a veteran soldier into a member of base staff. A manufacturer, a scientist, a radio dispatcher, or a driver perhaps.
You could make it so most of the soldier's former class experience doesn't transfer, and/or you have to pay for new cybernetic implants, if any.