Can I attach multiple phone numbers to my iMessage account?

So here's my predicament:

Any time I go travelling somewhere, I like to buy a local SIM card so that I don't have to pay fees for roaming data. The problem is that whenever I insert a new SIM card, iMessage switches to using my new (temporary) number and disconnects from my old (permanent) number. So any new messages I send will either send from this foreign number, or from my email; either one is inconvenient because it tends to start new threads for others in group messages and such. And people who try to iMessage my permanent phone number end up having it fail and then send it as a text message (which I will not receive until I get home and switch my SIM card back).

Is it possible to have multiple phone numbers connected to an iMessage account? (Without resorting to something drastic like buying more iPhones just to have more active numbers.) It seems like something that should be possible, but I can't figure out how to do it.