Hmm, that's a difficult question to answer. It depends a bit on you, your work schedule, any personal trips, how you work, where you're applying. For example, if you're pretty stable in terms of work over the summer and you're applying to schools that have similar strengths and requirements, then you might be able to stack a bit more closely. If you're applying to schools with entirely different applications - for example, HBS and Booth, then there are no economies there for you to take advantage of.
ON A SIDE NOTE - 6 to 10 IS A LOT OF SCHOOLS! If you're applying to more than 6 total, that means you haven't been thorough enough in your school selection due diligence. Anything north of 6 is asking for a lot of pain.
So if you apply to 6, you'd want to start...now. You have somewhere between 3 - 4 months depending on the school and it'll take time.
Bhavik