Never say never as there are certain combos of NES ROM and mapper that could be exploited to make such a thing.
For anything practical. Nope. Only time you will see true general multicart that works for basic hardware is for things based on CDs/DVDs/optical media or some newer types of systems, and even those have issues on occasion.
More old school stuff that leans into its carts to give it extra functionality and runs as close to the metal as you can get... trying to smash two games together if they are not of the correct type is a possible hack but generally considered a nightmare one*. Such that "get a better emulator", "get a better flash cart" or if it is ten patches to one game then maybe "get a better patching setup" is the order of the day.
*games use pointers to tell it where things (text, graphics, level data, music...) are, where to go in code and other things besides. There will be thousands, and may even be calculated in real time by the system (see relative pointers and pointer maths in general, though this is not as common on the NES as later systems). You then get to change one or both games to sit in a different location on the ROM, and add a tool to select which one you boot. The simpler stuff tending to be for the simpler games that don't have complicated mapper arrangements and thus you can use one of the more exotic mappers to switch one out and boot to another game. If one of the games (or base game in this case) is not of the simplistic variety, or one of the hacks makes it a complicated one (mapper changes are possible, indeed often done to allow the more simplistic games the fun features of more exotic offerings), then you get to go manually through said thousands of pointers, jumps and the like (including checking for maths, though it is reasonable to do what you can see and do a playthrough afterwards to see what falls over and correct accordingly, especially for the NES where most games are start to finish rather than jumping around all the time).