So I seem to be stuck with no possible way to progress really.
I've been stuck at 10 influence for a long while, and none of the hints to progress influence help.
The hints are:
School Board - punishment oversight
Miss Newman - advanced techniques
Miss Potts - settle / tender / strict.
I'm stuck at needing to advance priti and rachel's quests, but that I cannot do until I have 11 influence. What do?
Most of the people who end up with 10 influence do so because they took the easy way out and only got 1 point from Wilson. I haven't tried to progress that way, so not sure how that would work in the recent update (I am not sure if the staff training with Debbie unlocks in Chapter 1 or not) but you can check out the walk-through, it is very detailed.
The content you get from tricking Wilson (in addition to 2 influence points instead of 1) is worth playing.