... Is it possible to upgrade with some other RAM that has the same specifications, and if so, which specifications need to be matched? Bandwidth? Timings?
For example, could I add Corsair PC4000 2x1GB 3-4-4-8, or would the difference in timings be a problem?...
The Corsair PC4000 you mention should be no problem. The system will just run all the RAM at the speed/timings of the slowest installed RAM, and with both having PC-4000 speed and CL3 timing, the slight slowdown to 3 4 4 8 shouldn't be noticeable..