I'm currently in a graduate masters program applying to various PhD programs in my field. For my letters of reference I am using two references from my undergrad and one from my masters program. The graduate professor I am seeking letters from I know very well... indeed I know him the best of any one in my department. I got an A in his class last semester, I have worked in his lab since the beginning of 2015, and I did a four week internship with him over the summer. I recently asked him if he would submit letters of recommendation on my behalf to about 7 schools. He responded that he would be happy to submit letters for me, but to no more than about three schools.
I have no other real backup for a 3rd letter and am not really sure what to do. My other two letter writers are on board, but without this 3rd letter I can't submit my applications to more than three schools.