Sure, I guess you could play it back and forth like your sibling comment implies, that seems risky though (you might end up with no offers).
Also why do I want to stay with the cheap people? They proved to be unable to deliver market rates for my efforts unless I make a big scene about it. I don't like to do business with people like that.
There might be other factors at play, though. Like one company I stayed at for a while was only a lovely 45 mins walk from my house, and that was excellent for my mental health every morning and afternoon. Trading that for an hour in the car would mean I'd want more to offset it.
