Can someone assist me with how a refinance for my income property can work for me to buy a 2nd property?

My triplex initially was valued at $277k and I did a 5% downpayment of $14k, $263k 4.75% 30yr loan. Now 3yrs in and it's valued at $320k, remaining loan at $250k. I want to do a refinance and use the equity to put into a downpayment for a 2nd property, that I hope to get for roughly $200k at about the same rate.

I expect that I'd have to keep 20% equity in the home, so that out of the total equity (320k - 250k = 70k), I would need to downpay an additional 50k to bring it up to the total downpayment of 64k (20% of 320k) , which would leave me with 20k cash out to work with.

Am I looking at this the right way, and would it be worth it considering closing/legal costs? Happy to take any advice on the topic!