The SGX, as it is, does not have a larger colour palette or anything. It's just a PCE with extra RAM, twin VDCs, and a chip to control the priority of the two VDCs' display.
AFAIK, the switch on the back of the SGX disables writing to the 2nd VDC, making the first VDC's registers mirrored just like the standard PCE.
Space Harrier is one of the few games that will not work properly on the SGX, until you switch it to PCE-only mode, then it will work just fine. I just tested it.