jefro -- Thank you so much for the link. It was just the sort of information I hadn't been able to find on my own -- though askubuntu.com seems a pretty obvious resource, in retrospect, and I wonder how I managed to miss it.
Anyway, the linked page itself had good information, and it also had several links pointing toward different sorts of other helpful information. Somewhere in all that, I got it that I could use Windows plus Logitech's unifying software to unify my devices to work with the single receiver. I still had to spend about an hour on the phone with Logitech, because Windows XP, the tech finally divulged, doesn't have innate support for USB 3, which Logitech's receivers are designed to -- use? I'm not sure of the proper verb there, since I don't quite understand it. Finally, we downloaded extra software and got the devices unified, and, serendipitously and unexpectedly, the unification carried over to the Linux machine.
I'm very pleased to have success.
Thanks again to you and to everyone else for your help.