If your wanting to just have 3 displays at once, for office tasks you either need two GPUs, in either crossfire, or SLI, or you need a HD5xxx GPU supporting eyefinity, which will allow for 3 displays to be used at the same time. You could also require a new PSU to power it as well.
If your intention is to game with 3 displays your going to need major GPU horsepower to achieve this, so your looking at a minimum of two HD6870/GTX460 1GB's, a new PSU, and most likely a new case and motherboard (as its doubtful a HP motherboard will support CF or SLI setups). If your looking to game on 3 displays with full HD resolution your talking over 5000 pixels wide, by 1080 high.
So whether it is possible depends on your budget, and your intended usage. Two high resolution displays are more than enough for the majority of desktop office based activities though.
There might be other ways of achieving this, but in my opinion your cutting corners any other way.