Like many other families, mine doesn't react well to the news of "left overs" I use the "planned overs" system, which I assume is the same thing as the "left over layering". It works so well for us, I love it!

For chicken, this is what I do:

When I roast a whole chicken or bone in chicken breasts, the left over meat is shredded or diced then either frozen, used for another night's meal, or made into a freezer meal/starter. Even the chicken carcass/bones is saved for homemade broth/stock.
With the left over chicken and/or broth, I can make Chicken and dumplings, chicken pot pie, chicken and dressing, chicken tetrazzini, country casserole, chicken and rice, chicken casseroles, creamy chicken and rice, chicken stew/noodle soup, chicken quesdillias, burritos, enchiladas, tacos, bbq sandwiches, even chicken and biscuits...the possibilities are limitless...
Chicken thighs, legs, or quarters can be used in the same ways.
We usually use the quarters for baked bbq chicken. The left over meat is shredded and used for bbq sandwiches another night or frozen for a freezer meal for a quick meal.