LazySageDao
Solo looks better, managing a team is like managing multiple protagonists. If team members don't have strong personalities, it will only spoil the story. Having the mc venturing out alone, going through big meetings and breakups in their adventures, sometimes joining a team but never permanently would be better. Just use WMW Leylin as an example, the mc could be a more ethical Leylin.
Borrowing from the idea of creating an empire across dimensions, he could create a "company" where he can recruit talents across the dimensions that will deal with the miscellaneous stuff that will inevitably popup. It could be like in the Stargate Series where many small teams travel to another planets to explore and obtain information. This way he can travel alone or with different teams to be a pioneer to new dimensions (worlds) and leave the small stuff to other teams. It would give you a lot of flexibility to start plot lines and include an occasional character or maybe regular/main ones, but it could also be very hard to manage what every character is doing.
A small team is better on my opinion, having people who you can trust and delegate roles would be better than every time he goes to a world he would have to come from ground zero with everyone, someone like Tonks for example would be good from when he needs someone to infiltrating places or be some kind of bodyguard that change forms and will be impredictible and someone like Hermione would help him in take his burden from minor researches and given him a different outlook, it doesnt need to be then but I think those roles would be important an MC that can do everything become too much a "perfect being" that it becomes difficult to relate, no one is perfect and time is limited, besides it would be good to have the mc interacting with people who he really cares for a change, it would be good have some character development.
To be honest, I would prefer that the MC travel alone at the beginning. You know, mainly to gain experience in travel between dimensions. So at least the first or the first 2 trips you do alone. Also, since you already confirmed that you are going to make Hermioni part of the team, you have to take into account her personality and I do not mean the erudite part. You said yourself that the mc is not going to influence the canon much so the characters will retain their original personalities a lot. Hermioni will be very influenced by Ron and Harry, she will not leave her home world so where her friends and family are, she will even try to invite them since they are the golden trio for something, they are brave and bold. I would leave her in the home world and after the first trip I would try to influence her as well as other characters. So the mc would have a united and reliable team with which to travel and there would not be so many doubts. I mean no matter how smart and trustworthy someone looks, it would look unnatural if they were suddenly followed to other dimensions without much hesitation. Unless they were his slaves. Yeah, a lot of text.xd
why doesn't he make a empire he can fall back on when he needs help or inspiration. there's no need for him to rush all over the place, he's only 20 with possible immortality In the work. he can relax, get a foundation, get expireance with leading (delegation etc.) then go on a adventure in a new world. plus when he has roots in a new world he can set up a base for his empire to expand.
He doesn't trike me as having a team, more of having enough power to be able to not rely on any more. At most he will establish some power\group\organization in each\some of the worlds he goes to. For information gathering, money, etc. Maybe finding like minded scientists\wizards but under the capacity of employees. If he meets someone special enough maybe.
Assembling a team makes me think of him as a pokemon master. Seems like a lot of work with marginal benefits if they aren't very powerful and only the dark/grey sides would really be okay with his morals. Get him a smart wife (or wives if you prefer) and maybe a research team. As a recommendation, Fleur is always my favorite in HP universe. Smart, hot, prideful in a cute french way, loving towards her family and she goes for his age group anyway since he is only two years older than Bill Weasley. Full veela rather than quarter or whatever since it doesn't make any sense that there are any full blooded veela if they don't have male veela. The only way partial veela ancestry works in my mind is if a veela has a male child and then that child has a daughter making her quarter veela. Also, just imagined Hagrid being shown the pokemon world.