As other have said, you can absolutely add tomatoes, but then you will be making tomato soup, not chicken soup. (There aren't many soups you can add tomatoes to that won't just become tomato soup.)
- Saute two large yellow onions in a bit of oil.
- Add 3 units (+) of chopped or crushed garlic. (From a jar OK but not as good.)
- Add 3-4 stalks chopped celery. Reduce heat.
- Add any other compatible veggies in the fridge. (Optional.)
- Add 2 heaping spoons(*) of fresh rosemary and 1 spoon of basil. Stir through.
- Add 106-ounce can (!) of crushed tomatoes. Stir through.
- Add 1 quart stock, broth, or water. Bring to a boil.
- Add 3.5-4 pounds chicken, cut bite size, or equivalent amount fish or tofu.
- If chicken or fish is raw, stir until pot boils again.
- Simmer for half an hour to an hour.
- Serve over rice, steamed whole grains, or cubed toasted bread. Cheese optional.
This is very close to Portuguese-American gazpacho or this one(not Spanish gazpacho which is a cold tomato-cucumber soup).
This would probably also work with beef, meatballs, beef marrow bones, etc - they have a stronger flavor that can stand up to the tomatoes better. (Still trying to recreate my mother's beef tomato soup...)
- (*) Decide for yourself if it is teaspoons, tablespoons, or quarter cup. :-)
- (+) Decide for yourself if it is cloves or heads.
- (!) Standard US large can is 28 oz. This recipe makes a large batch. Leftovers good, freezes well.
Prompted by some conversation in comments, I found a Manhattan Chicken Chowder recipe! (The well-known New England clam chowder is cream-based, Manhattan clam chowder is tomato-based; I'd never heard of chicken chowder, but:)
Manhattan Chicken Chowder Recipe -- chicken broth, root vegetables, canned tomatoes, diced cooked chicken, thyme