I strongly dislike how one can change the Great Old One they are serving for free. I also dislike the idea of making it “often” or some other time related activity, because it reduces potential strategy. Thus I present the following possible fix:

Add the following to the end of Rule 2.12 but before Rule 2.12.1

If a student whishes to change the Great Old One they are currently serving, they must make a comment to the GNDT of DICEN DICEM where N is eir current mythos and M is the mythos of the Great Old One they are serving. If the result of the DICEN check is greater than the DICEM check, the student escapes free of harm. If the result of the DICEN check is less than or equal to the result of the DICEM check, the student must following “Leaving” instructions of the Great Old One they are currently serving. Either way, the student’s Great Old One is set to “-“ and e may change it to any other Great Old One free of harm.
If a student no longer fits the requirements to serve a Great Old One, then they are free to escape without the DICE check. If, however, a student no longer fits the requirements to serve a Great Old One and yet fails to make eir escape within twenty four hours, any other student may perform the dice check for em, and enforce the penalty if the deck check fails.

Add the following to the end of Rule 2.12.2

Leaving: Any student who wishes to escape the grasp of Cthulhu and fails the dice check gains X thirst where X is the result of the DICEM roll minus the result of the DICEN roll.
Mythos: 10

Add the following to the end of Rule 2.12.3

Leaving: Any student who wishes to escape the grasp of Nyarlothotep and fails the dice check must discard one tome of eir choice. If e does not currently possess a Tome, e must have eir mythos reset to ten(provided it is at least ten), and e loses X sanity where X is the result of the DICEM roll minus the result of the DICEN roll.
Mythos: 20

Add the following to the end of Rule 2.12.4

Leaving: Any student who wishes to escape the grasp of Azathoth and fails the dice check must roll a second DICE2. If the result of this dice check is a one, e stills escape free of harm. If the result of the dice check is a two, e is captured by Azathoth and has eir sanity reset to -60.
Mythos: 15