Financing a second property

[Hector R.]

Hello,

First post, so I apologize if this is two place to put this post. 

So I bought my first property with an FHA loan in 2019, I was luckily enough to find a below market 2-family short sale in north jersey. Since then I have put a lot of work into the house. I would like to implement the BRRR strategy, and buy another property to live in, and rent out the current one, I am planning to do a cash out refinance in the next few months, and then I would like to finance the second property using a residential mortgage, live it in while I rehab it. I would like to buy another two-family home, as I can used the second unit to help pay for the mortgage. However I was told by a lender I spoke with that I would only be able to finance a one family home. Is there any situation I can finance another two family using a conventional loan.

Thanks