If I added a field in the profile page that would allow classmates to identify themselves as band alumni or football alumni or such, is there a way some kind of identifier could be added to the "Classmate Profile" page so they could be sorted into that kind of sub-group?

No. But it's a good question, and one that has surfaced here before. We're going to create a make your own icon system definitely some time this year. There's so many other important things happening here we just haven't gotten to it yes. But yes, it's a good suggestion, and once implemented you'll be able to create your own icon, upload it to the system, and tie it into whatever Profile question you want.