Advice for aways is pretty specific to the individual. There's a reason most people only do 1-3: the more you do, the tougher it is to remain on your A+ game for what is essentially a month-long interview as fatigue sets in. But as a DO student, aways may be an important way for you to get your foot in the door at institutions that historically do not take many DO residents.
The other factor to consider is that aways are a double-edged sword. You can showcase yourself and wow a program, but if you look better on paper than you perform in person, it's worth considering whether maximizing aways is really the best strategy for you.
But as far as being worried that the specialty itself frowns on doing more than 1-2 aways:
a) I don't know that that's true, and
b) Interviewers have no way of knowing how many you do unless you outright tell someone at an interview.
So I wouldn't sweat it.