Not sure that you could upgrade to a later Mac OS X or macOS than Lion 10.7.5;
but the hardware can support other systems of appropriate compatibility to the
architecture. Some versions of Linux for Mac; or with a 'virtual machine' software
it may be possible to load other OS into the Mac. The limit is with Lion 10.7.5 in
use of 'virtual machine' software.
Several other computer systems could run on the Intel-Mac series of that vintage.
Later macOS/X installers and drivers likely aren't matched to work in MacPro1.1.
That said:
Upgrading the Mac Pro 1.1 2006 in the standard way using the ... How to upgrade
Mac Pro 1.1 from OS X 10.6.8 to OS X ... A possible solution is to run the download ...
superuser.com/questions/704751/how-to-upgrade-mac-pro-1...
Modernizing the 2006 and 2007 Mac Pro to Go ... to run modern versions of OS X on
the Mac Pro 1,1 and 2 ... Mac Pro 2,1 firmware update for the Mac Pro 1,1; ...
lowendmac.com/2014/modernizing-the-mac-pro-11-and-21/
... 1,1 (that has been flashed to 2,1 firmware). youtube 17min
Someone may have figured out how to tweak the firmware for a later Mac OS X.
And then you'd have to source a later OS X. ~ I don't know about that aspect...
Good luck & happy trails! 🙂