cash out refi in excess of DTI?

Yes, it can.

Maybe you could find a lender who'll lend without an Aztec Recognition Agreement with the co-op, but don't plan on it.

You'd have to lie to the coop too when you apply to it for a refinancing. It might work to give an allowable figure and then try to slip by a larger figure when it comes to closing and the managing agent doesn't notice. Or it might not.

Thanks much.

Years ago I had lenders that would not require an Aztec signed agreement. Don't know if they're still doing it.
A 25% DTI is rather low. Are you certain?

Maybe it's 28%, not sure, but still below what I'd like.

Don't try anything sneaky , you'll regret it