That's not okay, surely? Is there anything I can do about that sort of behaviour?

No, it's not okay. The time for this buyer to have negotiated was before he bid on anything at all, that way he could have made you some total offers which you either accepted or rejected.

At this stage, what you have is one sold item. I'd stop communicating with the buyer just for now, you've explained your stance and you haven't accepted his second offer, so that is off the table.

He will either pay for that first item or he won't. He probably won't, so as soon as the 4 days are up, I'd open an unpaid claim against him and this is when I would message him to explain that you understand he does not wish to pay but you need to open the case only in order to get your ebay fees back on the sale.

Of course, block him from any future bidding and then relist.