Is it appropriate to ask for more than one recommendation letter from the same person
Is there some reason to think that the professors will need to write different letters of recommendation for the different universities?  If not, then the additional incremental effort of sending the same letter to several different places is minimal.  Though I am not a professor, my role is similar, and I, at least, do not mind when somebody wants me to send the same letter to a handful of different locations.  If you were applying to 20 places, that might be a different matter...