I had an idea where someone with high level abilities in separate schools of thought could have access to abilities outside of either school.
For example a high level Pyrokinetic and Telekinetic may gain access to a concentration ability that allows to place an area/wall of flame which deals Telekinetic and Heat damage to everything that enters the effected area. Using their Telekinetic ability to feed the flames with atmospheric oxygen and hydrogen to help sustain the flames makes them a bit more powerful than a regular fire could be used as an explanation.
Meanwhile someone with a high Vitakinetic and Electrokinetic ability could drain batteries in their inventory to temporarily regain stamina or boost their recovery rate, potentially having a crash later.
Maybe a Teleporter and Telekinetic can redirect incoming projectiles with a chance to hit the shooter/thrower, higher levels increasing the impact and accuracy.
A Telepath and Photokinetic could subtly alter their appearance and aura to appear as an Ideal Person to an observer, maxing out their perceived Beauty and Intimidation to a single target.
A Biokinetic and Vitakinetic may unlock a concentration ability that slows the gain of Attunement and increases the rate of loss of Attunement, maybe at the cost of additional stamina cost to abilities.
Or alternatively can utilize Gained Attunement to cast abilities, reducing attunement but causing some detriment (Maybe pain would accumulate while concentrating, making it an emergency type ability)
As to the prerequisites for these abilities it could track individual powers or just the level of the passive abilities of each school (Which are based on the highest level power in that school already)
Maybe they could only be unlocked by studying research from the labs or only used by equipping a crystal of one of the appropriate schools.