With this design, I connect the sewer hose to the black gate and dump. When that is finished I remove the hose from the black and put on the new grey gate. I suppose you can get a wye connector to tie it all together but that's a little more than I was shooting for since I use the grey to rinse the hose after dumping the black.
My original thought was use a rhino flex wye
Connect one of the claw sides to the black, have a "jumper" hose to connect between the modified grey grate and the other claw end of the wye. Then finally connect the sewer hose to dump it all to the end of the wye with the bayonet nubs.
This might not work perfectly gravity wise because of the wye, dunno. So maybe two jumpers are needed like the pictures depict on the product page.
I abandoned the idea of hard plumbing the grey to the black gate because squarely between my grey and black gates is the hose holding tube so it would be blocked. Sure, I could walk around the trailer and fetch it from the other side, but I'm lazy :-)
*edit after your picture
This should work. You'll need short a 3" hose with one end with claws (grey gate side) and the other end with bayonet fittings (wye side). Just hope that gravity is on your side and there's a downward slope from the grey fitting to the wye