Does refinance at a higher interest rate makes sense

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Would there ever be a time when refinancing at a higher interest rate would make sense?!

I want to free up my fha, so I can purchase something closer to work which is less than 100 miles from my current house. I can refi my current home as an investment at 4.2(1.3 higher than my current house) and get another home using fha to my new primary