No. Two bases plugged in at the same time will "fight" and possibly/probably work worse than what you have now.
When you say they have trouble communicating in certain places in the basement, the remote and the base are both in the basement, right?
I'm struggling with how (what should be) passive filing cabinets above the layout/remote/base could affect your signal.
(Unless it's just a coincidence - are you sure your basement where you have the base plugged in has a good ground at the outlet? That problem has been documented in other threads)
-Dave