One PC can have multiple IP's and if connection is started from outside this PC will use both IP addresses.
If connections are started from inside, one PC will always use one of its (possible) many IP's. So @week's comment above is correct, to identify to outside world with 2 different IP's in the same time simplest solution is to have 1 real and 1 virtual PC, and you can then in virtual start second browser or just configure a proxy for second browser on your real PC.
Other solution is to have 2 real PC's, where second PC you would use just as proxy for your working PC. Today this is usually overkill, but if you have 2 old PC's with small amount of RAM, this is better (read: faster) solution than having virtual server on a PC with low RAM.
