Cash out refinance, get maximum credit. Refinance immediately?

[Rian Ash]

I currently have an investment property with 4% 30 yr fixed. With 75% LTV, I can get around 65K cash out from it. When i look to refinance, I see that for cash out the rates are slightly higher. At 4.5% I get huge credit which covers all the costs and gives me enough to pay the HOA fees for few months.

Question- After getting the huge credit, can I refinance immediately? If yes, going a step ahead, Can i start the new refinance application even before the current one has closed. I want to do this to give me a better chance to lock the low rates?

Thanks for your response!!