Latest OS X I can install on Mac Pro 3,1
The Mac Pro 3,1 [Early 2008] Can quite happily run the current OS X - at time of writing El Capitan 10.11.3.  I have one here running just that.

As of Sierra, 10.12, the above still remains true, yet further clarified - El Capitan is the final OS to support the 3,1 [&amp; indeed 4,1 unless it has been firmware updated to 5,1]

I would, however, be wary of such a long jump in one go. Be certain you have an up to date backup &amp; be prepared for the fact that a large number of your existing apps, if they are the same age as the OS, will also need updating.

I would also make sure you have a tested, bootable, recovery path should anything go wrong during the update. I've never managed to get a 3,1 to boot from USB; I've always needed a ready-prepared second HD. These days, that's just the recovery partition on my Time Machine drive, but 10.6.8 doesn't have a recovery partition.

For belt &amp; braces, I'd clone your exiting drive using something like Carbon Copy Cloner then remove it, so it doesn't cause confusion.

Wish you luck.