Variability in playstyle is a hallmark of the combat system in Crimson Tactics. Your units are allowed to change their Classes as much as you desire. It is showcased here.
Accessing Class Change
Class Change can be accessed through the Unit Condition screen of every unit found within the Party Management System.

Changing Class
In order to change your unit's Class, you must first acquire a 'Class Mark' for that Class. This is the currency required to change classes and can be found across the Shops in Wendalle or after battles as loot.
You must select the Class you want to change the unit to via the carousel where you can view various bits of relevant information such as Attributes and Usable Gear.

Class Stat Changes
Every Class has certain basic Stats that it inherently possesses. As units level up, they gain stats based on that Class's traits. However, if a unit changes its Class, its Base Stats change even though the stats it gained on leveling up remain.

