Am3+ with the 8320 will run at a max of 2000mhz.
You can run 2400mhz ram on it but it will downclock speed automatically.
You will get far tighter timings at the lower speed though to compensate.
I know it's been a while since the question was asked but I did recently purchase the ASUS 970 Pro Gaming Aura and it does state in the manual that it will support up to the 2400MHz. I personally do not have that in there, however it seemed to be intended as an overclocking rig for the AM3+ socket. I pesrsonally run the 8350FX black edition 4.01Ghzin it myself but have yet to approach the overclocking. It does seem that the support would be there since it is a stable OCer.
Bojangle12 :
I am looking for motherboards that can handle DDR3 2400 mhz memory. Its for an FX 8320. Its an AM3+ socket. Anyone know?