AGENT WANTS ME TO BID AGAINST MYSELF ON BUYING A 4-PLEX

[Burt L.]

I am running into this frequently and looking for a way to work around. In a strong local market, income properties are often listed in stating that offers are being taken for x number of days, and acceptance will be x number of days afterward. This drives me crazy as the listor is looking for more than the list price regardless of whether there are other competitive offers or not. 

On this 4-plex, I made a full price offer with no buyers side commission payable, title insurance and closing costs buyer paid,  no appraisal contingency, and sent a copy of bank statement showing more than sufficient funds for cash puchase (account number redacted) with a 12 day closing and an inspection clause. I made the acceptance date prior to the end of the timeframe offers were being accepted to see if it would be taken, and there was no response- as suspected. 

The end if the period for taking offers is end of business today and I have a message from the broker wanted to see if I am interested in the property, ignoring the fact I had already submitted an offer, which deadline has passed. 

At $700K with no buyers side commission (representing myself as I now do) and title insurance closing costs buyer-paid, I was already $20K higher on a net sheet to the owners- and still they are looking for more on a new offer. 

How can I break through this ongoing approach of trying to get me to out-bid myself? I dont know if there are even any other bidders, though it will be insisted that they exist. I would like to ask for a copy of the other offers, with entities redacted, but the broker will claim to be offended by this. Some brokers will even say that they had so many offers that they are asking one more time for highest and best to bring it further up, with no evidence that such offers exist. 

How can I find out what they really need to make this work, without the exercise in salesmanship? Broker has left a message asking if I am still interested - while ignoring my first offer - with the end of business today being a deadline for offers. I'm trying not to build resentments.