I got everything set up with my three letter writers, sent packets to them, sent reminders, and now the deadlines are approaching. But I got an offer that is really hard to refuse: A professor at my current program graduated from my top choice school and has a good relationship with my faculty of interest at the program I am applying to, and he has offered to send a letter on my behalf to this program. Such a letter would be a boost to my application, but I cannot add an additional recommender to the application. I have already entered everyone else into the online form and they have gotten request emails. The department says that letters must be sent online.
Can I ask one of my other writers to forgo sending a letter to this particular program so that I can use the alumnus's letter, or is it simply too rude ever to un-ask such a favor?