It doesn't taste as good as my usual stock
Do you have and uncooked chicken or turkey, and aromatic veggies
( carrots,onions,celery,fennel,etc) that you can simmer in the clam juice? Don't add tomatoes or things that will discolor your stock. It may not be pure seafood stock, but it will definitely add ooomph to clam juice.
I would def go with the same veggies as mentioned and uncooked chicken (preferably with bone-in) to work this out. Good luck!
A ham bone could work as well
If you are going to include shrimp in the cioppino, you could make a shrimp stock with the shrimp shells. Saute shrimp shells with some onions, celery, carrots, bay leaf, garlic, and tomato paste. Add water, and simmer.
Got any anchovies? One or two added to the stock toward the end can really boost flavor.
Also you can reduce the clam juice by a third to concentrate its flavor. To my mind, you can make a pretty good cioppino with clam juice only, provided the rest of your fish is flavorful. Personally, I would not bother with adding any other meat to the broth. Reduced white wine also can add an interesting flavor angle to the broth.