My experience eating at hole-in-the-wall restaurants in Shanghai is that they put the menu up on a big board on the wall where everyone can see it. That tier of restaurant doesn't give you an individual menu. So the number of items is limited. You don't order a permutation of options; they list options and you order one of those. Some things come in multiple options (e.g. 孜然牛肉盖浇饭 "cumin beef served over a bed of rice", if present, is likely listed alongside 孜然羊肉盖浇饭 "cumin goat served over a bed of rice"), but those are just separate (adjacent) entries on the menu, not a "pick your meat" kind of thing.