No such thing as a Bose half amped system, all Bose systems are fully amped, only the non Bose is half amped. Is the buzzing present on radio/CD?
If it is then it really depends how the Kenwood is hooked up to the rear/sub amp. If it's buzzing then there's a good chance it's via a PC9-401 adapter which uses a line-out converter to take the speaker output back down to pre-out level. Have a look behind the HU and if the adapter has a chunky thing on it wrapped in foam then that's the PC9-401. Just replace this with a PC(-404 which uses the rear RCA's instead, far better solution, or rewire the rears directly too the far superior amp inside the Kenwood.