There is no way that one chicken would last that long with 4 people eating. A meal, then hot sandwiches, then a casserole? You have GOT to be kidding—from one chicken. Must have been fed growth hormones to make it the size of a turkey!
Sure you can. I do it all the time, at least 2x a month especially in the winter. 10 lb chicken - Sunday, roast chicken (mashed potatoes, gravy, stuffing, vegs). In a day or so, hot roast chicken sandwiches, use up the rest of the stuffing, and mashed potatoes. Pick it apart with your fingers, getting any decent sized pieces off and tearing them up. There’s your casserole pieces, say with bowtie pasta, mixed veggies or throw some broccoli/cauliflower/carrot chunks in, some frozen peppers from the garden, any gravy leftovers. Maybe a can of cream of chicken or mushroom if it’s thin, a can of milk and bake. Just like those frozen bags of skillet dinners you can buy now but much, much better.
**THEN**, you take whatever is left. Bones, meat, skin, bits of dripping off the serving platter and throw it in the stock pot. Chop up and throw in an onion, several large carrots and stalks of celery, some buillion. Let it simmer for awhile and cool, then strain. There is still going to be a ton of meat there, most people throw it away. You have to pick through it with your fingers, throw the scraps away (skin, bones, squishy carrot, lol). When you’re done, you have enough stock for a soup or stew, along with meat already in it. Cook some diced up carrots and potatoes, frozen peas and top with biscuit dough when it’s boiling and you’ve got stew with dumplings. Or cook it in the oven with crust and you’ve got pot pie.
The turkey that fed us for 8 days was 25 lbs so I had more to work with. People throw away an awful lot of meat with the carcass if they don’t stew and pick it. Sometimes I’ll just stew it and get my stock then freeze that until I’m ready to use it. There are usually at least one or two meals left on the birds when most people throw it out. I’ve been doing it for 23 years, as my mother and her mother did. It can be done.