Sounds like a doctor prescribing someone with an occasional, small blister on his foot a third, prosthetic leg that you have to wear always. You will not walk any faster, only the chance that you might stumble will increase! Costs a lot of money too.
Did the it-guys have to fix a lot of problems because of non-sw software crapping up your systems?? It's the only argument I think of that could justify such an investment. The perfomance argument can be ignored because it is solvable with a good multicore processor and lots of memory as other people pointed out.
If every year you cannot use your system for about five hours because of non-sw software causing problems, and taken in account a three year period of use, one can buy a acceptable new system (five hours that you are not working and five the it-guy has to spend on your pc makes 10 hours of loss). I assume the return money on your old system is more than cancelled out by the energy costs of running an extra pc with screen (sharing one screen is very impractical imo), extra datatraffic hardware, more importantly the hours that IT has to spend to setup AND support all extra systems, cost of extra software licenses, extra time and maybe annoyance too to switch between pc's over and over again.
If you want to discourage IT, put in the right numbers to make your calculation show that it is a crap idea.
Then propose to spend a fraction of that money on backup-software and an extra harddrive to put on several periodically taken images of your systemdrive. If you experience slowdown and suspect non-sw causes, you have your system running smoothly again within ten minutes.
have a nice weekend, pietje