I have put multiple speakers in series on a single speaker-out from an amp before. It works okay, but it is quieter. What would be more effective would be to find three speakers of a lower resistance... they are usually 8 ohms, but I think there are 6-ohm speakers too, and possibly even lower resistances. Then you'd have 18 ohms or less to drive instead of 24, if you put three in series. You also might find something like 16 ohm or 24 ohm speakers, which would produce an 8 ohm equivalent load put in parallel, and look like a single speaker to the amp circuit. The amp might have trouble driving three 8-ohm speakers in parallel, but then again it might not. If you don't care about the amp, you can try it. You can also try locating the components that provide the power, probably a large transistor with a metal backplate, but there are many other sources of amplification that are harder to identify, and add extra cooling to them. If it's a transistor-powered amp, adding the extra cooling on the transistor and putting the speakers in parallel would probably work fine.
The best bet to get three speakers to be driven from one speaker wire is to get an amp that can supply a lot more volume than you want to use. Like, my cab amp is unpleasantly loud with its volume knob 1/3 of the way up. It wakes the neighbors upacross the street at half volume, and begins audibly rattling the windows and knocking loose objects off tables at 3/4 volume. (full volume has never been tried, for fear of never needing a stereo again the rest of my life) So putting three speakers in series would just make me crank the volume a bit more to get comfortable volume.
Keep in mind that computer speakers are built to be integrated systems with no unknowns - not like home stereo amps where you're supposed to be able to get your own choice of speaker. So, changing what's on the speaker wire may throw the rest of the circuit off and make odd things happen, so don't expect sure-fire good results even if nothing burns out. I don't think problems are likely, but I've asked Boston Accoustics engineers about using some of their PC satellites in special ways before, and they have cautioned me that they don't behave like "normal" home audio speakers, and plugging them in to any system but the one they're designed for is iffy. He even claimed that substituting other speakers for the satellites would not work. (in my system the satellites are nothing but speakers - the amp and everything else is contained in the sub)