Sadly your system is limited to El Capitan OS-X 10.11.x as Core 2 Duo CPU’s are limited to 32 bit as the systems BIOS (EFI) is not 64 bit clean. As long as you understand this is as far as it will go I would just focus on Maxing the RAM and upgrading the drive to a SSD.
If you really want to upgrade the CPU you are limited to what Apple used in this series [https://everymac.com/ultimate-mac-lookup/?search_keywords=iMac9,1|iMac9,1]. I’m not sure if it will support the Intel 2.8 GHz Core 2 Extreme (X7900). It won’t support the Intel 2.53 GHz Core 2 Extreme (QX9300). Frankly, I don’t see this as that beneficial given the limits of the rest of the system.