Assuming you need a mortgage to buy the new place, probably not. First banks require 6 months of reserves for both house payments to avoid a buy and bail scenario. Some people have used the scenario you describe as a way to get into a better house and then once the new house closes, stop payments on the first house. Underwriting has gotten really tough! Also renting to a family member might be construed as not an arms length transaction. This scenario depends on so many factors. Job history and reported taxable income, Debt to asset ratios and of course credit score. For sure it would be easier to buy another house if you sold this house first. Banks scrutinize everything nowadays.
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