Izumi Midoriya
Quirk - Progenitor: Allows the user to sense, form connections, and control blood.
Auxiliary Ability - Crystallization: Allows the user to harden controlled blood into crystals. Any crystallized blood will return to liquid once the control is released.
Auxiliary Ability - Blood Hunter: Allows the user to have heightened sense of sight, sound, touch, and taste while quirk is activated. As a permanent side effect the user will be able to see the blood flow within others.
Auxiliary Ability - Overdrive: Allows the user to temporarily empower themselves and the blood they control. Requires a lot of stamina and is physically exhausting to use. Overuse can cause the main Quirk to temporarily enter a dormant state to stop the user from accidentally causing their own deaths.
Auxiliary Ability - Regeneration: As long as the user has enough blood within their system they can regenerate from nearly any injury. Anything that would destroy the entire body, remove a limb, freeze, or burn the body cannot be regenerated.
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Ochaco Uraraka
Quirk - Gravity Manipulation: Allows the user to manipulate the gravity of anything they touch. Losing concentration or putting the tips of their fingers together will undo any gravity changes on those things.
Auxiliary Ability - Orbital Tether: Things under the influence of the main Quirk will stick nearby the user. This does not include anything experiencing the full power of the quirk (i.e. full removal of gravity or gravity being intensified to a high degree).
Auxiliary Ability - Visual Manipulation: Allows the user to manipulate things within their sight, however the effect of the main Quirk is only about half as strong on things that have not been touched.
Auxiliary Ability - Telekinesis: Allows the user to control the objects under the influence of the main Quirk. Requires concentration and is mentally draining.
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Katsuki Bakugo
Quirk - Explosion: User sweats nitroglycerin and can ignite their sweat from anywhere in or on their body.
Auxiliary Ability - Internal Combustion: Allows the user to ignite an explosion within themselves to give them more physical power. Constant use can cause damage to the internal organs so it must be used carefully and not in rapid succession.
Auxiliary Ability - Flashpoint: Allows the user to pool their sweat into a single point for stronger and more concentrated explosions.
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Tenya Iida
Quirk - Engine: The user has engines somewhere on their body (calves in this case) and can use said engines to increase their speed. Fuel for the engines is the food they eat so quality of the food is important. However because of this the quirk quickly drains stamina.
Auxiliary Ability - Overgear: Allows the user to shift beyond their normal speeds. Excessive and constant use will cause irreparable damage to the engines themselves.
Auxiliary Ability - Boost: Consuming a special type of fuel can cause the engines to enter a state similar to Overgear but without receiving damage (in Iida's case the special fuel is orange juice but it varies from person to person).
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A/N
I just wanted to include a quick list of the changes I've made to quirks and the additional abilities I've added. To be clear Auxiliary Abilities or not additional quirks. Rather they are facets of a quirk that can be unlocked through training and expirementation. Having more Auxiliary Abilities does not make one stronger. Bakugo is a prime example, he only has two but is roughly the second or third strongest within Class 1A at this point.