In Gmail, when I get a second (or more) message in from the same sender, they stack. Some of these I want to keep one message, and archive the others. Also I need to label them differently sometimes.
How can I deal with stacked messages separately?
You don't have to use Google's Conversation View if you don't want. Then you can do whatever you want with individual messages.
I've looked into solutions to similar problems before, and I think that the problem is that the threads system is so entrenched in the software that it's difficult if not impossible to organize your mails in any other way.
A less than optimal way of dealing with it would be to forward the messages of the thread to yourself, and in doing so, change the subject line to fit them into your own organizational scheme. This loses the sender information, but if you wanted to separate all of the emails from Jim Smith about billing, then forwarding them to yourself with both of those items in the subject line would preserve it. Extra credit if you make filters to do all of the dirty work.
There may be a "Labs" feature in the works for this kind of thing, but I putter through those periodically, and I don't recall this ability in any of them.