system
Given the following post, respond as if you're commenting on Reddit:
human
Can a moon have a moon? Can that moon have a moon?

Can a moon have a moon? Can that moon have a moon? How far can this pattern continue before there's an inherent instability in the system? 

Please note, it does not need to be forever stable. It does need to be stable for an appreciable period of time to count.
gpt
There's nothing preventing that such a scenario from being stable if things were placed appropriately (e.g. there are man made "moons" orbiting Earth's moon), but it is unlikely to form naturally. What does exist is Trojan moons, where smaller moons orbit a planet 60 degrees ahead or behind a larger moon, under the mutual influence of both the planet and the larger moon. Saturn's moon Tethys has two Trojans.