What is the upper bound of number of stable interacting stars in a star system? I remember very well reading in an article that it's impossible to have a stable star system of 4 or more stars. The article justified its claim discussing about the complexity such systems would have in terms of mass, velocity and distance to be stable. Further more I think there was a constriction related to our 3-dimensional universe, unless I confuse it with an other article about why solar systems cannot form in 4 dimensions... I don't remember though where I read the article.
And since then I thought there couldn't be star system with more than 3 stars and that belief was enforced with the movie Contact when Jody Foster traveled through space and encountered a quadruple star system. What an opportunity for a movie to claim the existence of something so exotic, right?
Recently there's been a fuss about the TIC 168789840 six-tuple system. So either I'm very behind in astronomy news or I confuse the terms Star System and Solar System in the article I read...
Here an article about the aforementioned system.
There is no true upper bound. You could argue that a galaxy is a vast multiple star system, with hundreds of billions of stars. Natural galaxies are not perfectly stable (random encounters eject stars over very long timescales), but one can construct stable systems by taking pairs of similar-mass binaries and placing them into a remote circular orbit around each other. This can then be repeated indefinitely, with $2^n$ stars forming a vast system.
In practice such neat systems are unlikely to form naturally (4 levels seem to be the max observed and often involves very unequal masses) and very wide systems will encounter other stars often enough to be destabilized. Eccentricities tend to have a triangular $f(e)=2e$ isothermal distribution, making things less stable. See (Duchêne &amp; Kraus 2013) for more statistics.
(As an aside, Jaron Lanier and Piet Hut have suggested constructing such vast hierarchical systems as a clear indicator that there is intelligent life present.)