At the moment I would prefer just one character per player, as the RP is intended to be focused around a small group.

Generally speaking, there are three things that allows a student to take lessons in the Esoteric Schools of magic. The first and most obvious is simply being a well-known and long term student of the college. The students who don't really bother to stand out in any positive way at the school will often be denied access to the Esoteric schools simply because the college doesn't know them well enough to trust them with such magics. 

Secondly, it requires sponsorship from an organization outside of the college. There's a lot of backdoor politics about the Esoteric schools of magic, so basically anyone who wants to learn them must be held responsible by either a reputable organization or even a government. Aka if the Fantasy CIA of the Elven Kingdom sends a letter to the college and says "this person is going to be one of our agents and we want them to learn Necromancy". 

And the last is simply testing and passing to show you do have the ability to control the various magics of the Esoteric school. Usually this is simply a show of magic ability that you would presumably have learned and honed as you were taking primary schools, but it can also rely on how well you respond to magic of the esoteric school as well. So if you want to be a necromancer, you'll be tested to see how well your body and mind handles having your life energy directly manipulated, since that's a thing that Necromancers will do. Or if you're going to be a telepath, how well your mind handles being invaded or constantly hearing everyone's thoughts, emotions, and so forth, often over the course of a few days or even weeks.

Magic itself is already dangerous for people who only have an academic knowledge of it, and even well practiced mages must be careful not to over do it. The Esoteric school is even more dangerous not just because of the power they wield, but also because using them generally is more threatening to the user than the primary schools. There's a very real possibility that even if you have enough control over magic not to suffer from blood sickness, the spells themselves could end up doing yourself in if you aren't adequately prepared to handle them. But again, that's what the school is for, and why most students would never really touch the Esoteric schools beyond whatever they may research on their own time. Naturally, you as players could be the exception if you're willing to take on the trials to learn. But don't expect this to be a thing you can do right off the bat.