Preheat oven to 350°F. Grease a 9 x 13-inch baking dish or spray with nonstick cooking spray; set aside.
In a large Dutch oven or large skillet, brown the beef, bacon, and onion over medium-high heat until the meat is no longer pink. Drain off excess grease.
Add the pork and beans (with their sauce), kidney beans, navy beans, and lima beans.
In a medium bowl, whisk together the ketchup, brown sugar, vinegar, and mustard.
Stir the ketchup mixture into the bean mixture. Season with salt and pepper to taste. Transfer to the prepared baking dish.
Cover with foil and bake for 25 minutes. Remove the cover and continue baking for about 20 more minutes, or until hot and bubbly.
Notes
Alternate Slow Cooker Method: Just keep in mind that the Crock Pot beans will have a more "soupy" consistency. First, brown the beef, bacon, and onion on the stovetop as instructed. Transfer the mixture to a Crock Pot, and stir in the remaining ingredients. Cover and cook on HIGH for 1-2 hours or on LOW for 3-4 hours. Remove the lid during the final 30 minutes to allow some of the steam and condensation to escape and the sauce to thicken.
If you like more sauce in your calico beans, leave the cover on the dish for the entire 45 minutes.
The total cooking time may vary. For really soft, broken-down beans, cook the dish for 40 minutes covered, and then remove the cover for another 20 minutes.
For added heat, season the beans with Cajun seasoning or Creole seasoning, some hot sauce, or a dash of cayenne.
Do not drain off the sauce from the can of pork and beans. The other canned beans should be drained before adding them to the pot.