Max wasn't idle during the years before the entrance test he had nezu handle a couple things for him such as nagant being recruited and himiko toga being taught to control her tendencies and how to use chakra. although she was being taught she was on a career path of an underground hero like eraser head since she was built more for stealth and infiltration missions. being taught chakra gave her more kick to her attack capabilities but she was no jounin-level more like she was around academy or genin-level.
Nagant on the other hand was being rehabilitated by nezu in a secret facility, so she wouldn't be around until the middle of the school year and by that time she would be an additional teacher authorized by nezu.
speaking of nezu otherwise known as rat satan he had made great impacts on various people thanks to the information max has given him, being more of symbol of fear for people doing unethical practices such as those who ran the facility that max and himiko was found at and himiko's own parents they were drowned in humiliation and dishonored heavily making them laughing stock and scorned individuals making them flea the country but the facility organizers got thrown straight into tartarus.
max had been training all his abilities from basic ki usage and basic chakra usage to a state where he was able to duplicate any jutsu up to b-rank and was able to use any ki ability that was introduced in regular dragon ball but anything from z or kai up was beyond him at the moment.
at some point nezu requested all might to test max's physical capabilities on a desert island and the results were astonishing as when all might used an all out smash max just just caught his fist making him slide back only slightly, and anything else didn't even faze max as they traded blows going tit for tat causing huge shockwaves to blast from each blow. all might quickly got tired and his time limit ran out revealing his frail form to max. max just shrugged already knowing about it from his previous life's memories then proceeded to use a super charged healing jutsu to reverse enough damage to enable all might to lengthen his time limit to four or five times his prevous limit then informed all might that any further would require more training seeing as he had yet to use any a-rank jutsu and barring that s-rank once he could use all jutsu healing all might would be a walk in the park.
nezu and even nighteye was excited at that news when all might and max returned from the desert island but still swore max to secrecy regarding all might's weakness, needless to say max didn't mind as all might was a decent distraction to any villain that would seek max out should he reveal too much of his power. all might on the other hand was glad and relived that there was such a promising and strong hero that could even give him a run for his money among his son's generation.
nezu often times wondered where such a young hero got all his infomation from and max just replied "with my super hearing i can hear anything even a pin drop on the other side of the world." nezu was shocked to say the least but was reassured realizing that max wouldn't turn evil. On the other hand the underground group that ran the hero organization had a headache constantly from nezu thanks to the info from max preventing them from doing their usual dirty work.
~~~~now~~~
Max sighed as he looked around surprised that two class 1-a originals were missing their place in class replaced by himself and himiko, the students being koda the animal and bug whisperer and kaminari the electric dunce. (spoiler alert ahead for those who hasn't went past deku's vigilante arc) he wasn't surprised by mister navel lazer being here even though he told nezu about this traitor becuase he also informed nezu it wasn't by choice because his family was held hostage, so their plan was to ignore his dubiousness until they rescued his parents.
max scoffed clearly disgusted by all-for-ones methods no matter how effect it was, looking around further he was surprised by one change in canon... todoroki wasn't a he but a she...weird, must have been the R.O.B.'s interference. max knew things werent as simple as canon such as there might be more then the original villains not just all-for-one's future vessel's league among that nine and the other scums he read or watched about. Yes I-island is plot this time and he was invited along with all might's family due to his friendship with them not to mention the second movie which was about gene activation or something like that.
Sighing internally as he felt someone cling to his right arm as he looked at himiko who blushed and turned away, an unavoidable consequence of fixing her life is that himiko fell for him and considering even nagant had some signs of a crush too he decided he'd only take at most three if he ever got a harem. why three and not two? well even before he got reincarnated he was dead set on one person. looking toward tsuyu who quickly looked away he mentally simped but was outwardly calm... yes he had a thing for the frog girl but who knows if it'd work. he did some searching and found that those with strong enough quirks were encouraged if not forced to take more then one spouse but that law was somewhat old and overlooked and it was limited as well.
Max sighed again as the early warning bell rung causeing himiko to let go and sit at her desk which she chose the only one next to his as he sat right next to the window in the rear of the class. when the final bell rung he noticed catapiller-sensei slide into class across the floor which stunned some students who weren't as socially guarded as himself and todoroki shaya as he learned her name was from hearsay (yes i know i suck at names) when catapiller-sensei emerged from his cacoon his obviously bagged eyes studied each student before doing row-call. when he was finished he had the students ushered to the track and field for his olympic style quirk assessment.