Collaborative Filtering With 1 prediction per user

I have a problem that I see as a possible collaborative filtering issue and I wanted to get some thoughts from everybody here. My use-case is that I want to match a tutor with a student. So the problem I currently have is that each student has an average of just over one tutor that I can select from. So I am wondering if collaborative filtering is still possible in this case or if this is too sparse to be useful. The other thought I had was to maybe group students by some features before doing the collaborative filtering piece, but this might defeat the purpose since I would be losing a lot of my detail. My other option is that I will just use the information I have about each student and the information I have about each teacher as one line of data and then the output will the the rating that the student gave the teacher. That is my backup plan if I can’t find a way to do sparse collaborative filtering (if that even makes sense).