And even if you receive two or more offers at once, many organizations don't bother negotiating. One time I received two offers at once, and neither organization was willing to change anything substantive about their offers.

In this case, one organization had an onerous IP policy and that other did not. I asked for some carve-outs, and the first organization came back with a single line added to the IP policy that did not change anything meaningful. I told them that I could not accept that offer as written and wanted more changes, but they refused further negotiation and told me to take it or leave it. I waited a few days, rejected their offer, and accepted the other offer.

(I think that they were willing to add the single meaningless line to make it appear they were willing to change things without actually changing anything substantive.)

The morale of my story is that you may not be able to negotiate a better offer, but at least you have a choice when you have multiple offers.