They dont see where you've applied to until you do the FAFSFA, unless you tell them - there are a few secondary applications which do ask, on those, I just listed a couple schools (mainly because there wasnt enough room to list them all)..specifically schools in the local region of the asking school...So, it shouldnt be a red flag. They know its competitive anyhow.
If you can afford it, apply to a bunch. Better to apply to too many than too few. I'd apply to the schools you are most interested in first. If you get into one of those, you can avoid interviewing at places you aren't that into. After getting into 2 of the 3 schools in my top 3, the only other interview I attended was a school ~1hr's drive from home.
I submitted my application before I had my MCAT score and it wasn't worth it to risk missing a year... so I probably did overkill. I applied to most everywhere (on primary) except 2-3 schools due to tuition or otherwise. I ended up having a pretty competitive application, but I can't say that I wouldn't do it again. Yeah, it cost a lot, but it is better to be safe than sorry. Some people in my class it was their fourth time applying and I'm of the belief that if you can get in the fourth time, you likely could have gotten in the first time.
I plan to apply to like 13 schools. Western, KCUMB, KCOM, DCOM (LMU), LECOM-Erie, LECOM-B, UNE, Touro NY (Although looks super ghetto), VCOM, PCOM, GA-PCOM, PCSOM, TCOM.
Its not that I can necessarily afford to apply to all these schools, its more of the fact I am at a huge disadvantage as it is applying as a Canadian from a Canadian University....AND my gpa is low.
My point: Might as well apply broadly, see what interviews you can get, if you get multiple interviews you can choose which ones to attend based on cost etc, and finally if you get multiple acceptances you have more pull in your future. Spending the extra money is worth it in the long run, because you never know where you could get accepted unless you apply