Yeah, it's generally called ["scalability"](https://en.wikipedia.org/wiki/Scalability ).

For example, you can't generally scale-up a machine by just multiplying all of its dimensions by, say, 2, and expect it to still work the same way. Ditto for organizations.

Scalability would generally be a problem even if you could ensure that the sorts of people involved wouldn't change. But, if you're considering a scenario where the the types of folks involved also change, then that'd probably tend to amplify the effect.

That said, systems can often be scaled-up with due consideration to how they work and ensuring that the fundamentals are kept.