Lending Limits: Even with sufficient capital and low DTI ratio

Hello everyone. After spending a few years following BP I've finally completed my first rehab and flip and now I'm looking at multi-family units to buy and hold.

I'm wondering if anyone has run into difficulty getting a conventional FHA loan even when they have plenty of capital for the down-payment and a low debt to income ratio?

The Plan:

My goal is to purchase two 4-unit buildings in the next 12-18 months with each property costing around $200k. Thanks to my flip and other savings I have enough capital on hand to put 20% down on the mortgages. With my current salary I will also be able to keep my DTI at less than 40%.

So far so good!

Everything looks fine on paper, but since I don't have previous rental experience I'm wondering if conventional lenders will be reluctant to hand out a $320k loan to a new untested landlord. 

I'm curious if you guys think I should only expect to get approved for a loan on one 4-unit right now, and I'll need to prove my landlord worthiness for a year or 2 before I could get another.

Thanks for your sage advice!