Arduino 2560 as an Interface to 4 Serial Hardwares
No, but it is possible to use 3 of them. The reason being that one of them is the connection to the computer.

The hard part is in the programming. You will need not only a suitable sketch on the Arduino (the easy part), but also some software on your computer that presents three COM ports to the operating system and forwards the data through to the Arduino in a suitably packeted format, and receive data back and sent it on to the right COM port.  Depending on your operating system that may be a very easy task (on Linux and OS X) or a complete and utter nightmare (Windows).