Remove the old box and enlarge the opening
As a general rule, a standard 18-cu.-in. box maxes out at three 14-2 cables. (The box size in cubic inches is marked on the inside of the box.) The easiest way to accommodate the fourth cable is to install a larger box. However, you should check with your electrical inspector for a permit and approval.
Stop at a home center and buy a double-gang “old work” box (also called a “remodel box”). You can install a second receptacle in the larger box and cover it with a two-receptacle cover plate. Or you can stick with a single receptacle and use a two-piece “snap together” cover plate (with one receptacle and one blank).
Start by turning off the main breaker. Then remove the existing receptacle and use a tester to make sure none of the wires in the box is “hot.” Use a fine-tip marker and tape to label the wires that go to each wire nut so you can keep them straight later.
Turn off the circuit breaker to the box before beginning any work.