Combine chicken, beef shank, veal, water, and seasonings in an 8 1/2-quart stock pot. Bring to a boil; cover and simmer 2 hours. Remove chicken, beef, and veal from broth. Remove meat from bones, and cut into pieces. Return meat to broth, stirring well.
Add remaining ingredients. Simmer, uncovered, 2 hours, stirring frequently.