running more than one server with one IP address

[David Banning]

Is it possible to run more than one server(machine) with one IP
address? I have so many different server-applications running on my machine I
would like to divide them up.

Maybe using one machine email only, or use one for certain websites,
and another for other websites. This would also allow me to take-down
one machines for maintenance when necessary, or use one machine for
more troubleshooting.

Wondering if someone could even direct me to the terminology that I am 
looking for so I can google it.

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