In my personal experience, this doesn’t even work across two different intermediaries when you are already in the bank’s system. The honor/commission belongs to the one who established the first contact. The intermediaries knew from me that I was also exploring other options and always took into account where I was already known. Because it doesn’t make any sense otherwise.
At one bank, I was in the system through an intermediary, but the project fell through there due to the stupidity of a bank employee from somewhere else. I then went to a local branch here, where the stupidity was, as expected, not present; the colleague from somewhere else saw this in the system and put a stop to it. Then the two argued, and I signed somewhere else.