Power strips make this easier of course, but every outlet usually has two plugs and most* of the time they are wired together. You just need to plug into the other plug.
* In case they are split for whatever reason (switched plug, different circuit) whatever, just take off the faceplate, pull out the outlet, and now you have direct access to the screw terminals and copper wiring on the outlet. You could wire into the plug using the second set of terminals or via the other connection method (one being the screw terminals, the other being the "insert into the hole" depending on which is used) and take the whole outlet with you.