You could use Velveeta. I used the processed cheese my father-in-law gives us which he gets from commodities.

Did some adjusting to come up with a quantity to can. The below recipe makes about 1 gallon of soup:

Ingredients:

1 tbs olive oil
1 large onion chopped
2 cloves garlic minced or 2 tsp of minced garlic
1/2 tsp dried oregano
6 cups chicken broth
4 cups chopped tomatoes
8 cups of shredded zucchini (use a food processor)
2 15.25 oz. can whole kernel corn
16 oz. of processed cheese cut into small cubes

Directions:

Heat the olive oil in a stock pot, add the garlic, onion and oregano and saute the garlic and onion until tender.

Mix in the chicken broth, tomatoes, entire contents of cans of corn, and zucchini. Heat at a high simmer until soup is thoroughly hot while stirring occasionally.

Mix in the cheese. Continue to cook and stir until cheese is melted. Serve.

I have 3 gallons of shredded zucchini in the freezer and my plan is to make enough soup with that to can 21 quarts with some left over for a meal. I won't add the cheese while canning. I'll add that later when I heat the soup. I figure about 4 oz of cheese per quart of soup.