Subclassing is a game mechanic introduced in Etrian Odyssey III: The Drowned City, and also available in Etrian Odyssey IV: Legends of the Titan. Subclassing gives limited access to a second class for any unit, granting a more varied moveset and opportunities for class hybridization. In both games, this mechanic is not avalable from the start, instead it's unlocked by story progression.
In EO3, subclassing is unlocked after reaching the 3rd Stratum. It allows for almost complete access to a secondary class' skills, with the sole exception of their class passive; this includes weapon mastery skills, which means that a class can gain access to alternate weaponry and shields from their secondary class. Five skill points are granted after choosing a secondary class. Subclassing can't be done from the Explorers Guild, instead it's done from the Celestial Palace.
In EO4, subclassing is unlocked midway through the 3rd Stratum, by completing the Rise of the Baboons quest and defeating Kibagami. Unlike in EO3, here subclassing exempts both class skill and Sky skill, while also halving the second class' skill caps; since there are no weapon mastery skills, any character gains access to alternate weaponry (and shield, if possible) upon subclassing. At the same time, once subclassing becomes unlocked, all party members gain the ability to wield 2 weapons. They still only carry out their normal attacks with their main weapon, but their second weapon becomes their sub-weapon with which they can use weapon-requiring skills, so that the character can still perform their subclass' weapon skills without worry of needing to switch each time. Subclassing is done from the Explorers Guild.