Now B contacted me, not yet ready to give an offer, but they mentioned that their offer would likely be significantly larger if they would be able to see the of

Now B contacted me, not yet ready to give an offer, but they mentioned that their offer would likely be significantly larger if they would be able to see the offer from A in writing. I see nothing but red flags here. It also sounds like you are already dabbling with a bidding war... you are holding back on A, B knows about A, B is "offering" to out-bid A. Now you are wondering if you can leverage a questionable offer from B to up A's offer. If you escalate this further into a full out bidding war, the probability is high that it won't turn out well. If B wins, you work for a sketchy company just for the money... or they don't come through with a real offer, A drops out (note that you do not have a formal offer from A yet), and you are screwed. If A wins, the person you work for knows what you did to them and resents it. Sorry to be harsh, but from the outside looking in, B sounds pretty sketchy and your line of questioning doesn't reflect well on you.