My offer on a REO was rejected as too low - the issue with the townhouse is listed at (1)"system did not hold pressure due to damages, unable to find source of allleaks, water heater damaged at side where TPR valve damaged" and (2) "Water Supply and Sewage system was inspected for presence of obvious visible defects.

THEN, the bank reviews the owners position, then does a BPO, then accepts/rejects/counters.

I expect them to reject any reduction which means I may need to walk away or accept a decent to good deal that may be a great deal years from now  

I would not bother saying no because I would be rejecting his application to rent.

I have a Bx 3 fam fully renov asking for alot more than that. i rec'd and rejected a higher offer than your  $536k. 

You are still allowed to reject that unauthorized roommate if you find criminal or other negative findings from the screening.If you decide to approve the new tenant, just draw up a new lease for a 1 year term (or your choice) with the new rent and make sure all roommates are included on the lease. easier that doing addendums for rent and roommates etc. and you get them to commit to a new 12 month lease so you dont risk move-outs in the middle of winter.

It makes me wonder if they have already tried and have been informed that they are not eligible, or rejected mitigation offers or didn't comply with the terms.

Should I show him the recent sales from the Clerk of Court office if he rejects my proposal?

I don't want 3 couples + children living in the property, but if all of their background checks out and I reject them because of the size of their family then surely that's discrimination??

If the only issue on their loan approval is that you don't yet own it (meaning the appraisal, prelim, and contract, will all be rejected), that means you can safely take ownership.