I'd hope no later than May 28th or 31st, but getting the clear to close doesn't have anything to do with your closing date, as you get the clear to close once all documents the underwriter needs for final approval have been submitted to them and signed off on. Of course the goal is for that to happen before you are supposed to close. Speak with your loan officer about what remaining conditions are still outstanding and what the plan is to satisfy each of them and you'll get a better idea of when that'll be.
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