The School of Transmogrification teaches transmutation generally, but with a particular focus on magics that alter the form or physiology of living creatures to improve or extend function.
Most Transmogrifiers prefer to overcome obstacles via the expedient of enhancing however many creatures in whatever ways necessary to render the obstacle trivial. This predisposes them to wanting companions to experiment on. Or, uh, aid and enhance. Let's go with that.
Recipients of spells cast by a Transmogrifier that grant beneficial physical abilities take on minor cosmetic variations suggestive of the boon they have been granted for the duration of the spell. For instance, a target of Expeditious Retreat, Longstrider, or Jump has longer or more muscular (or even animal-like) legs, a target of Enhance Ability takes on ursine traits for Bear's Endurance or feline traits for Cat's Grace, a target of Spider Climb takes on spider-like traits, and so on.
Choose two Wizard spells from the Transmutation school, each of which must be no higher than level 2, and add them to your spellbook for free.
In addition, whenever you gain access to a new level of spell slots in this class, you can add one Wizard spell from the Transmutation school to your spellbook for free. The chosen spell must be of a level for which you have spell slots.
Choose a number of Transmutation spells in your spellbook equal to your Proficiency Bonus, that are no higher than level 2, and have a casting time of an Action, a Bonus Action, or a Reaction.
The chosen spells are always prepared by you but do not count against your prepared spell limit. You can swap one of the chosen spells for a different eligible spell after finishing a Long Rest.
You also have a pool of magical power equal to your Proficiency Bonus. You can expend a use of this pool to cast any one of the chosen spells at its lowest level without a spell slot. You regain all uses of this pool when you finish a Long Rest.
When you cast a level 1 or level 2 Transmutation that requires Concentration, you can modify it so that it does not require Concentration and instead has a duration of 5d20 rounds (rolled secretly by the DM) for that casting.
This improves to include the next higher spell level when you reach Wizard levels 10 (spell level 3), and 14 (spell level 4).
When you cast a Transmutation no higher than level 3 that targets a single willing creature (including Self), you can modify it for that casting to target one additional visible willing creature within 15 feet of the first target.
This improves to include the next higher spell level when you reach Wizard level 14 (spell level 4).
You add the spell Regenerate to your spellbook. It is a Wizard spell for you, and you do not need to provide material components to cast it. When cast by you, this spell causes the skin and flesh of the target to take on a greyish green hue and to become tough and rubbery for the duration of the spell.