BRRRR + traditional funding simultaneously?

[Dina Hillier]

New user here! 

We have one rental property in Texas and just did a cash out refinance . (Our current tenant's rent is paying for total cost of new mortgage, including cash out)

We are currently looking at properties in the Cleveland area (my hometown). We have 250k to play with and are targeting a duplex as our 2nd property in the 200k range. We then plan on the BRRR method to continue expanding. QUESTION- Since I would qualify due to my income, should I simultaneously be getting preapproved for a traditional loan to expand at a faster rate? Or just stick to those original funds to start and see if/how we we can add a 2nd property within the next year. Thanks in advance!