There used to be ISA cards which gave you, in effect, a second computer running in the PC so that you had two computers for the price of one (plus a VDU and keyboard). I haven't seen any of these around recently and doubt they are supported under Linux.
Another method was a kind of 'reversed KVM' switch which connects two VDU/keyboard/Mouse sets to one CPU. Fine provided only one user wants the machine at a time.
Given the price of machines these days, though, neither of the above seems like a good move. Surely, all you want is a second cheap machine running Linux and connect it to your main machine using a serial cable (probably set up as a null modem).
You can even run X-Windows this way, although slowly.