Getting Pre-Approved for Mortgage Using Projected Rent

[Steven Lewis]

I am looking to buy a multi-family home. 

Simply put, can you get pre-approved for a mortgage for a "larger" amount using projected rent?

Example: Pre-approved for $200k for a single family home. Multi-family home costs $300k. Can you use the anticipated rent to get you pre approved for more?
If so, would it have to be through private lenders?

Any leads? I live in and looking to purchase in NJ.