Buy second primary home while refi for current primary is ongoing

[Sunny Er]

Hi,

Refi for my current owner occupied primary home is going to close 9/5. Can I get into contract to buy a new primary owner occupied house on 9/2, expected to close on 10/2? Different lenders. How will the new lender find out about the old refi? Can I say that I was just shopping for rates if new lender ask about the credit hit for the older refi?

What can go wrong?

Thanks!