You have to be a bit careful on that as the last thing you need is for the lender to find out after the refi and think that you never planned to stay as your primary residence. I did a loan for a client two years ago that I had done 4 previous loans for. The last loan i did for him was for a house as his primary. He put 5% down and we closed the loan. About 7 months later I got an email from my lender stating that the servicer for that loan, who was Wells Fargo, had gotten a loan application request from the same borrower at their local branch to buy an investment property and it listed his previous address as his current primary residence, not the one that I had just done the loan on 7 months before. Obviously they wanted to find out if he committed fraud on the previous house by saying he was buying as his primary when he actually wasn't. Truth is he DID intend to buy as his primary, because 2 months after we closed he called asking if he could get a construction loan for a $300k addition on that home which wasn't really possible given that the end value of the house just wasn't there. Never heard from him after that point, so when I got that email it was obvious that he realized the house wasn't worth the addition and just decided to rent it out and never actually lived there. The crazy thing is that prior to that loan, i financed a house that he bought as new primary about one year prior to that, where he did actually live. So when we did the loan that Wells was questioning, one of the underwriters conditions was a REALLY GOOD explanation as to why he was buying another primary residence that was literally less than one mile away from his current residence, which he also just happened to buy less than a year ago. We did have a good reason for it, so we were able to get the loan done. The guy was an honest guy, its just that his business was growing exponentially and from the first day that I started working with him, he always talked about getting his mansion. I believe that was the original plan with that house, but he realized after the fact that it wasnt the right house for it. So I wrote a long letter to Wells explaining why I believed it wasn't intentional and they ultimately backed off.
My suggestion would be to wait at least 6 months, or a preferably a year after you close on the refi before you start looking for another home. 1 year is kind the general rule, especially with FHA, although if you had to move because of a job or something that's obviously different. 6 months you might still be ok, but if you are planning on doing this 6 or 7 times, then you are probably asking for trouble. If that is your plan then I wouldn't be surprised if a lender or servicer eventually caught wind of it and realized that you had bought 6 or 7 primary residences over the past 3 or 4 years and considered that the same as lying upfront. That's just my two cents though...
