There wouldn't be anything automatic. If another team wants to make an offer then they need to make an offer in the system. Honestly you'd probably want to create a duplicate test league and try different scenarios to see how things work. I think your problem would be that each trade has to be voted on and so since the original trade was already accepted, would the system even allow another offer for the same players to be generated and how would it handle that one being voted on while the other is as well?
I'll be honest here that it all sounds like a mess. I personally refuse to play in any leagues that have trade voting of any kind. It's nothing but a nightmare as owners will vote no on a trade simply because one of the teams voted no on their trade last week or they will vote no not because it's a bad trade but because it makes a rival stronger. And then the timing, bad enough if I make a trade on Saturday to try to win this week but can't actually do that because the trade is hung up on voting for a week. I probably wouldn't even bother trading because why bother if I don't get my traded players for another week and in the meantime things may have changed, especially injuries.
My suggestion (and I know you didn't ask for it and I'm not saying you are "wrong" for doing voting) is to trash that whole system. If you want a gatekeeper for trades then that's the commish's job. All trades go to the commish for approval. Commish then approves and pushes it thru. Only veto for clear collusion or something just so bad you have to (like a kicker for a top 5 QB or something).
In my leagues the commish (me in one and my buddy in another, but we use the same rules) approves all trades. It's pretty much a rubber stamp, I've only vetoed a trade twice in over 20 years and none in the past 15 or so. We do have some checks and balances however. We have a 3 person Competition Committee of myself and 2 owners voted on each year at the draft. If I personally am not sure on a trade and want opinions I go to the CC for their input and then make a ruling. If I actually veto a trade then either owner can protest the veto to a CC member and force a league vote to overturn my veto, thus giving them a way to overrule a power hungry commish. We also have a rule for our trade deadline party for the "drunk trades", if the majority of owners protest a trade that went thru within 24 hours, then a league vote will go up to overturn the commish approval and veto the trade (has never happened, but again, it's there mainly to make everyone feel better and can be used if needed). It's suggested extending that to all season but the owners don't want to so we don't. But you could if owners are scared of the commish power.
End of the day, you either trust your commish to do the right thing or you don't. If you do then it makes a lot of issues like this easier. I've rambled on long enough. LOL