In my late game developed fort I have a king and a separate dwarf of course as broker and mayor. This summer I had an elf diplomat arrive, a human caravan arrive, a human diplomat arrive, and a human merchant princess arrive at the same exact time. Here's what happened.
First, the king met with the human diplomat. Meanwhile the merchant princess begins to attempt to meet with my broker/mayor. They do sort of meet, the broker's job is "Conduct meeting" and they get together in his office, but I never get the text screens nor do I get to negotiate the contracts. Meanwhile, I get the text screens for the human diplomat meeting with the king. I figure Ok, the game can only handle one meeting at a time, so everything will be cool when the king finishes his meeting.
Problem is the king finishes his meeting, then the elf diplomat who had been sitting on the map edge waiting on the king's meeting to finish comes to the fort and meets with the king. The king sleeps, eats, drinks, and finally meets with the elf. I get the text screens for that meeting, and work out the # of trees I get to cut this year. That meeting ends, and my broker is still in his endless meeting with the merchant princess.
There are no other dwarfs trying to meet with my broker/mayor as far as I can tell. He just eats drinks sleeps, and then goes back to his office to "conduct meeting" with the merchant princess, who follows him there no problem but I never get the text screens for the meeting. I imagine if this continues the merchant princess will simply go insane on me after awhile.
This is in version e, although I believe I genned it a version or two prior. It's somewhat modded and I no longer have the exact original raws I used, so if you'd like a copy of the save Toady I'm not sure how to oblige that.