I own one Windows 7 Pro OEM license and one Windows 7 Home OEM license.
The Pro license is currently in use on a computer that doesn't take
advantage of its advantages (specifically its RAM limit of 192 GB. My
new build-in-progress has the Home license installed but not yet
registered. I'd like to up the RAM on the new build to 32 GB, but I
know that Home is limited to 16 GB.

Is it be possible to de-register the Pro license from the old computer
and install it on the new build? I'd install Home fresh on the old
computer, of course. The hardware on the two computers is completely
different.