You are limited to the Haswell (4xxx) CPUs - there are a few that are slightly faster but it's not likely to be attractive from a price/performance standpoint.
There was a post where someone upgraded to a 4790K, which is the unlocked for overclocking version. Out of the box it is set to run at 4.0 Ghz, and will turbo boost to 4.4Ghz if one or two cores are active, or 4.3 if three cores are active or 4.2 if all four cores are active.
Compared to the 3770 which has the base CPU speed at 3.4Ghz and Turbo boost at 3.9/3.9/3.8/3.7 for 1/2/3 or 4 active cores.
So a slight bump in CPU speed, but probably not worth the investment.
If you do the upgrade you might consider upgraded the CPU cooler too. I did this on two of our 8700s and installed a cryorig H7. very nice upgrade, runs cooler and quieter.
If you haven't upgraded to a fast SSD, I'd start there.
What software are you running that needs more CPU?