To easily prepare the tomatoes, use a sharp knife and cut the tomatoes while still in the can.
In a large soup pot over medium heat, add chicken, beef, pork, 1/2 of chopped onions, and 4 quarts water; cover and bring to a boil, Reduce heat to low and simmer 20 to 30 minutes until chicken is tender and the meat falls from the bone; remove chicken from the pot to a large bowl and set aside to cool (when cool, take meat from the bones and cut into pieces). Refrigerate cooked chicken until ready to use.
Continue to cook beef and pork approximately 1 1/2 to 2 hours or until tender. Remove beef and pork from the pot to a large bowl and let cool (when cool, take meat from the bones and cut into pieces). Refrigerate beef and pork until ready to use.
Strain the stock, place in refrigerator, and let cool. When cool, remove fat from surface of stock. Return cooled and strained stock to soup pot. Add remaining 2 quarts water; bring to a boil. Reduce heat to low and add remaining onions, carrots, and potatoes; simmer 30 minutes or until vegetables are tender. Add chicken, beef, pork, peas, celery, tomatoes, salt and peppers; simmer until thoroughly heated. Serve in large soup bowls.