I doubt it very much.
I do not know the insides of MacPro's well but I might guess that you might be able add another Xeon processor or check on upgrading that 6-core CPU to something with more cores.
Knowing that that late 2013 Mac Pro is one of the newer "trashcan" models, you will not see much if any improvement in performance no matter what you do. This is because 64GB of RAM produces little tangible benefit over 32GB in Premiere Pro, and the Mac Pro's motherboard can only accommodate a single CPU - period. Plus, the GPUs are integrated onto the motherboard, and thus cannot be upgraded at all.
Worst of all, the newer Mac Pro's innards are mostly non-user-accessible. This means that you will not be able to access the CPU without special proprietary tools that few people have.
Thank you Randall for giving us the straight scoop!
I just read your PM. The CPU is technically replaceable/upgradeable (as that article stated), but (as with any OEM system) will void the original warranty once that is performed. I stand corrected.
Still, that late-2013 Mac has only one CPU socket on its motherboard.