Can a residential seller present a signed AOS to a buyer?

[Desmond Smith]

Hello, everyone.

I am trying to purchase a residential investment property from a finicky seller. We reach several verbal agreements, but they never return a signed AOS with those terms or submit counter offers. Some time passes after the AOS expires, and they will ask for a new offer (which they do not sign or counter).

We are on the third iteration of this loop and I assume they are just using the offers as negotiating tools to attempt to engage in a bidding war with other potential buyers.

My AOS's have all expired and I am not interested in writing anymore offers. Instead, I am considering asking the seller to present me with a signed offer when they are serious.

This may be an unconventional approach, but is it possible and/or reasonable? I'm in PA. 

Any other ideas? Thank you!