Refi primary residence

[Erandi Lechuga]

I would like to purchase a small multi-family loan in Colorado. A duplex or triplex that I can house hack. I have 20K cash but my primary residence has appreciated nicely and I'd like to re-fi to put a down payment on a multi family. I've been told I likely won't be approved for a loan after refinancing my primary residence.

Should I continue to save until I can afford the down payment or re-fi? If I re-fi, what are the chances I'll get approved/not approved for another loan?

Newbie asking for help!