Relay calls from one phone to another
Solution 1:
Yes - handsfree bluetooth accessories will work to extend the range a good 25 or more feet in many cases. You could also rig a wire and have much, much longer extension, but I can't imagine wanting to be wired to the phone and using a handsfree in that manner.
There are many, many mobile base stations that work with all manner of cellular towers and technologies, so those would be my next choice if you can't get the phone close enough to reception for bluetooth to extend the range to your body.