Is there any acceptable clause or stip to allow for making multiple simultaneous counteroffers, such that only the highest response from the buyers will be binding?

I have an offer on a house (I didn't get any closing concessions, but would like to counter offer) Unfortunately the seller also is wanting the due diligence and appraisal/financing deadline to be in 2 weeks which is impossible unless I am a cash buyer.  

I just signed papers on the sellers counter offer and I should close in two weeks.

Each offer I wrote recently which was more than 10% off list price has been rejected hard with no counteroffer given...2.  

I have never made an offer with anything less than 5K EMD, and the last two REO purchases I have had requested 10% EMD in their counter offers. 

If so was this submitted with your initial offer or with your counter offer?

We agreed to a counter offer on 4/5 (I was not aware of the entry of foreclosure at the time).  

The seller agent for this property won't schedule a viewing of the property, nor will the current landlord/owner/seller, but still expect us to meet their counter offer site unseen.

The listing agent told me that the lowest the bank would go was 165K, and he isn’t willing to take my counter offer to the asset manager or bank, but isn’t he required to take any and all offers??

I told him I could not get there and didn’t even bother to make a counteroffer.