I have in the past had my two - firewire - port - equipped Firewood hooked to two different computers, one old XP machine and a newer Win 7 machine. This stopped working for some reason after switching around things in my studio, though.
To answer your question, there are USB splitter type things, especially from back in the day when computers only had one or two ports. Many have six+ now, so they're not as common. I have one sitting gathering dust in my desk drawer.
Heck, I'd send it to you for cost of shipping, but they should be easily source able near you. You certainly wouldn't be able to have everything switched on at the same time or anything fancy...
Or you could just pull the plug every time you needed to switch. Not too hard, esp. if you have an extra cable.