We'll the most easy way is to install another serial port into your PC. You can buy one at a very low cost at your local PC dealer shop. I have installed in my computer 4 COM ports and 3 PARALLEL ports. But if you still want to make a multiplex, you have to make your own circuit or buy a ready made.

In general it is not difficult to make a serial multiplex circuit. Use some level converters to convert +- 12V RS232 signal into TTL level - like MAX 232 for TX and RX lines. And use one output RS232 line from your PC to switch to channel 1 or channel 2. This can be RTS line from your serial port. If switched low, channel 1 is selected, if switched hi, channel 2 is selected. At TTL level, you can use a standard multiplex IC like 4052 or 4053 to switch serial signals. You will also use external power supply for the switching unit.

If you prefer using uC, you can also do it and you switch channels using some ESC sequence commands, that will never be used in your normal communication protocol with modem or whatever other serial device you are using.