Aim for zero. Seriously. The faculty selection process is largely based on the interview. All of your written materials are designed with only one goal: to get you an interview. Once you interview, all of your written materials will be of minimal value, unless those materials “ding” you. Therefore, your strategy is simple: aim for zero.
Consider what those recruiting a faculty member want out of a candidate. They want someone personable and low maintenance. No department chair wants to recruit someone who is going to be a pain in their side. Your letters, therefore, should primarily speak to your collegiality. Therefore, you can get letters from three sources: supervisors, colleagues, and mentees.
Supervisors. See the above description of what a department head is looking for. If your current head can write that you are low maintenance and highly productive, that makes it easy to offer you an interview. If you are finishing your residency, obtain at least one letter from a faculty mentor, and preferably two.
Colleagues. This could be someone in your discipline and someone outside your discipline. If possible, a letter from each of these is ideal. It’s important to demonstrate that you can get on with others in your discipline as well as those outside of your discipline. You should definitely have at least one and preferably two letters from colleagues.
Mentees. These are preferably residents who have now gone on to bigger and better things. If you are an administrator, they may be faculty you have supervised. In general, it is better to solicit letters from people with whom you no longer work- that way there is no concern of inappropriate pressure applied to them. If you trained a resident, they loved you, and they are out in the world as a specialist, they have no pressure to write you a good letter except that they loved working with you. If you are a resident, a more junior resident or a former intern who liked working with you may be good. This category is not a requirement and these letters of recommendation should be considered additional to the core letters.
I strongly advise you get at least one letter from a supervisor and one letter from a colleague. You need people who will speak to your collegiality and productivity/work ethic. Ask potential writers if they are willing to write a good letter, send them the position description, and give them plenty of notice/time to put a letter together. Remember your goal: get an interview.