Promotion Branching is a mechanic that first appeared in Fire Emblem Gaiden.
Overview[]
When a unit performs able to Class Change into a promotion class, they may have several options that the player may choose to make them. In most cases, these are two options and at most four if promoting from a Trainee class.
In Gaiden, any of the Villager characters could promote into any of the base classes at the player's discretion. Since these were locked to male characters, their only promotions were Mercenary, Archer, Cavalier, or Mage. Its remake allowed female units to be Villagers with Faye as the only default fenake Villager. This allowed branching promotions into the generic female classes. All first tier into further tier classes are locked to a single path with no deviations.
Since Sacred Stones, in the subsequent games that featured this mechanic, promotion branching is done when promoting a character from a first tier into a second tier class. All promotions are fixed but the player is free to decide which promotion is made. Some classes do share one or both of their promotion options with another class such as the Cavalier and Knight class sharing the Great Knight class as a promotion option, but both having a separate one, such as their Paladin and General promotions respectively. Others have no unique promotions such as the Mage class in Fire Emblem Awakening sharing its Sage promotion with the Cleric/Monk classes while it shares the Dark Knight promotion with the Dark Mage.
For details on what classes' options are, see the respective class listings: