School of Spellcraft
Some wizards eschew specialisation in a particular school of magic and opt instead to study the underlying theory of spellcasting itself. Known as spellcrafters or sometimes 'savants', these individuals come to possess an intimate knowledge of how magical energy is channeled and manipulated. This knowledge allows a spellcrafter to make modifications to a spell as it is cast, and gives them an advantage when facing an opponent who also wields magic. Spellcrafters are considered to be bookish and academic even compared to most other wizards, although most will jump at the opportunity to discuss and debate magical theory. Spellcrafters often find themeselves in a teaching or researching role, and those who become adventurers often do so in order to investigate great arcane mysteries, or for the chance to perform important field work around a particular theory or subject.
Improvised Spellcrafting
At 2nd level, your knowledge of the workings that underpin spellcasting allows you to make adjustments to your spells as you cast them. When you cast a spell with a spell slot and the spell deals acid, cold, fire, lightning, necrotic, poison, or thunder damage, you can substitute that damage type with one other damage type from that list (if the spell deals more than one type of damage, you can change only one damage type per casting of a spell).
If you cast a spell with a spell slot that requires a saving throw, you can change the saving throw from one ability score to another. If the spell requires a Strength, Dexterity, or Constitution saving throw, you can alter it to require a different ability from that list. If the spell requires an Intelligence, Wisdom, or Charisma saving throw, you can alter it to require a different ability from that list.
You can modify a spell a number of times per day equal to 2 x your intelligence modifier (minimum 1) and you regain all uses after a long rest. Making major alterations to a spell is taxing on your body; if you attempt to change both the damage type and the saving throw of a spell at the same time, you expend two uses of this ability and must succeed on a Constitution saving throw with a DC of 10 + the level of the spell you are attempting to alter. On a successful save, you cast the spell as intended. On a failed save, the spell is cast in its unmodified form but you still expend the uses of your Improvised Spellcrafting.
Vexatious Incantations
At 6th level, your mastery of the underlying theories of magic gives you an edge against other spellcasters.
If a creature attempts to counterspell a spell that you are casting, it must always make an Intelligence check to do so, regardless of the level of the spell slot used. If you have modified your spell with Improvised Spellcraft, the Intelligence check suffers from disadvantage.
Shorthand Scroll
Also at 6th level, you become adept enough with magical notation that you can create special scrolls in your own unique shorthand. At the end of a long rest, you can spend 10 minutes with a quill and some paper or parchment to scribe a unique spell scroll that only you can decipher and cast from. The spell you scribe must be in your spellbook and its level can be a maximum of half your wizard level, or 8th level, whichever is lower. You must provide any costly components specified in the spell's description. Once you have cast the spell from the scroll, it reverts to being a nonmagical piece of paper or parchment.
You cannot have more than one scroll created by this feature at any one time. If you use this feature again while a previous shorthand scroll still exists, the old scroll loses its magic and becomes useless.
Prodigious Memory
At 10th level, your expertise in arcane theory allows you to recall spells on the fly. As a bonus action, you can replace one of your prepared spells with another spell from your spellbook. You can't use this feature again until you finish a short or long rest.
Additionally, when you use your Arcane Recovery class feature, you can choose not to regain any spell slots and instead swap out a number of your prepared spells with ones from your spellbook. The combined level of all the spells you swap cannot be more than half your wizard level, rounded up.
Master Spellcrafter
At 14th level, you can effortlessly modify spells of almost any kind as you cast them. You can use Improvised Spellcraft to modify spells that deal force, psychic and radiant damage types and you no longer need to make a Consitution saving throw when modifying the damage type and saving throw ability of a spell at the same time.
Additionally, any modified spell you cast using Improvised Spellcrafting has its save DC increased by 2.