The driver for the copier/scanner/printer is going to be the problem. I've
been there and failed because the driver for that C/S/P just took over
whatever resources that were available and kept them for itself. I didn't
try using a serial port for the second printer but that may work as will a
secod printer on the USB bus.
This is one serious failing of HP printers as they don't like to work with
each other.

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Why do penguins walk so far to get to their nesting grounds?