I think a lot of people assume a multiverse works that way because popular fiction makes it look like it does. However popular fiction is using something more akin to an omniverse (idk if there is an actual agreed scientific definition for a collection of multiple multiverses so Im just using that).

Using your analogy with the donkey kong discs being different universes with slight alterations in the warehouse (multiverse). In an omniverse scenario that you see in popular fiction, next door you’d have another warehouse but instead of donkey kong discs it is mario discs, or maybe donkey kong plushies.

However again that’s all speculative of if there even is a multiverse let alone something larger than that