I frequently wear a pair of Bluetooth headphones paired to a computer. If I want to listen to something on my phone I have to re-pair the device to my phone.
Is it possible, through software or hardware, to have both my phone and computer connected in such a way that I can get audio output from either device to my headset simultaneously.
Depends how much you want to spend. I wouldn't start the search with Amazon, take a gander at Head-fi.org forums.
Almost all proper headphones should support it, but it's worth verifying before purchase.
So you're better off shortlisting headphones you like, then narrowing by multipoint support, rather than only buying based on multipoint.
I use Sennheiser BT-4.50, and they support multipoint. (Frequently available on their outlet store for good prices). I'm almost certain any of the recent Sony XM range will too.