If you can operate off of a G4560 while on the H110 board you currently have then you're on the latest BIOS update. Just to be sure, see if you have an BIOS updates pending. You can then look towards any Kabylake processor part though mind you, you should not look at K suffix processors like the i5-7600K or the i7-7700K.
List your full system's specs like so:
CPU:
Motherboard:
Ram:
SSD/HDD:
GPU:
PSU:
Chassis:
OS: