Up to 10 per Fannie Mae guidelines. I just crossed the threshold of 4 about a month ago. Took a little patience because a lot of the larger banks and lenders (Chase, Wells Fargo) will still not do more than 4 but the lenders should be able to find you something.
My guess is that the banks are overcorrecting in reaction to what's transpired over the past year or so and that they are allowed to be more restrictive than Fannie Mae guidelines if they choose.
John J Mondello Jr, Realtor
"I find the house, you make it home."
There is more to it than that but I just wanted to give you the concept. Below is a link to a site where you can get some information. I have not used or worked with this company and I am not recommending them. I just liked their site.
Molly Thompson, Broker Associate APR