Serious Eats - seriouseats.com

There are so many types of soups and stocks, ham based, sausage based, beef, pork or veal, seafoods, vegetable stocks...
If your family is allergic to chicken and carrots, just omit them from a recipe. If your family member is not allergic to parsnips, they add a similiar flavor profile to a stock.

Rabbit makes a nice substitute for chicken in stock preparation. Much less meat, but still a good substitute.

Forgot to add...

Refrigerate for one week, or freeze for one month.

I have a large repertoire of homemade soups, but my favorite is based on a recipe that was published in the NY Times, and said to be over 100 years old. There are no meat products in it. It makes a spectacular, soufflé–like presentation, and tastes amazing.

Onion Soup Gratinée
6–8 servings Prep plus cooking time: 2 hours
1 bagette (stale is OK)
6 tbsp. unsalted butter, softened
3/4 lb. Emmental cheese
5 large onions
1–1/4 cups tomato puree
3 tbsp. Diamond Crystal® kosher salt
1/4 tsp. fresh ground black pepper
1/2 cup dry sherry

Equipment:
5.5–7.25 qt. round dutch oven
large saucepan
food processor w/shredding disk or box grater
rimmed sheet pan

Position oven rack to upper middle position, and preheat to 350°F. Slice the bagette into 1/2” thick slices. Place bread rounds directly on oven rack and toast until lightly golden (10–15 min). Transfer to the cookie sheet to cool.
Grate the cheese and reserve.
Peel and slice the onions. Melt 4 tbsp. butter in the pot over medium–high heat. Add the onions and sprinkle with the pepper and 1 tbsp. DCK salt. Sauté the onion until well caramelized (15–20 min), stirring frequently. If they stick, just deglaze the pot with a little water. Remove onions from pot and hold aside.
Butter the bread toasts on one side with the remaining butter, and arrange closely together on the sheet pan. Sprinkle all but 1 cup of the cheese on the buttered bread rounds and press down to adhere.
Arrange 1/3 of the bread rounds in a layer on the bottom of the pot. Cover with 1/3 of the onions, then 1/3 of the tomato. Repeat same layers two more times. Finish top with the remaining grated cheese.
Keep the oven at 350°F. and move rack to lower–middle position.
In the saucepan, dissolve 2 tbsp. DCK salt in 2 qts. boiling water. Stir in the sherry. Carefully pour the liquid into the dutch oven near the edge., trying not to disturb the top layer of cheese. Simmer on the stovetop for 20 min., uncovered, then transfer to oven and bake for 1 hour @ 350°F., uncovered.

Are your family members allergic to parsnips? Replace the carrots with parsnip. Or anything you want. I've made stocks out of just about all the root veggies available at one point or another.

The easiest answer is to make chicken stock, remove the chicken and carrot portions, and replace with whatever you'd like. Fish bones, shrimp shells, rabbit, veal, mushrooms (mushroom stock is a must have item), parsnip, turnip, fennel, and on and on it goes.

As CJ said, there are few hard and fast rules.