So I'm thinking maybe I can get a 4 channel amp, bridge two channels for the sub and run two speakers in parallel on each of the remaining two. Would that work?

It would work but only if:

a) The amp in question can have the rear channels bridged for a sub like that, and it has enough power to properly drive your chosen subwoofer in that configuration. Not all amps are bridgeable, and not all amps are good for running subwoofers that way. If you're not careful about matching the sub to the amp, damage to either the amp or the sub can result.

b) The front channels can handle a 2-ohm load.

c) The front speakers can operate correctly in parallel.

Another option would be to get a relatively inexpensive 4-channel amp (say, 30w RMS per speaker) and then add a self-powered subwoofer (for about $300). That's the way I had things going in my VW before the stereo and the subwoofer got stolen. It sounded great.

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Tony Fabris