The moon orbits Earth, earth orbits Sol. It's true that Sol orbits the galactic center, but that's not what this question is about.
Is it possible for a solar system like the Sol system, along with at least two more solar systems, orbit a single, more massive star? (Where we have a solar system of planets, this would be a solar system of solar systems.)
You don't have to look very far to find such a system. Proxima Centauri, the closest star apart from our Sun, has at least two exoplanets orbiting it, while this red dwarf star itself orbits a mutually bound pair of larger stars in the Alpha Centauri system.
There are also circumbinary planets that simultaneously orbit both stars of a binary system. The earliest known example is PSR B1620 with a confirmed exoplanet orbiting both stars. Such configurations are stable provided that the planet is far enough away to effectively "see" the binary as one object gravitationally. In this case, the exoplanet orbits at a distance of 23 AU versus the stars orbiting one another at a distance of roughly 1 AU.
In the known structure of the universe, solar systems, including our own Solar System, typically orbit individual stars. This is because gravitational interactions and the dynamics of celestial bodies generally lead to the formation of planetary systems around single stars.
The scenario you are describing, where multiple solar systems orbit a single, more massive star, is not a common to happen in our current understanding of astrophysics and cosmology. It would be highly unlikely for multiple solar systems to stably orbit a single star due to the following reasons:
Gravitational Instabilities: The gravitational interactions between multiple stars and their respective planetary systems would likely lead to unstable orbits. Close encounters between stars can disrupt the delicate balance of planetary orbits and eject planets from their systems.
Energy Considerations: The gravitational potential energy of a solar system is typically dominated by the central star. In a system with multiple solar systems, the gravitational energy of the central star would need to be much higher to hold all of them in stable orbits. This would require an extremely massive central star, which is not common in the universe.
While its not impossible to imagine such a scenario in a fictional or hypothetical context, it is not a natural outcome of the way celestial objects form and interact in our universe. In our current understanding of astrophysics, planets and solar systems primarily form around single stars, and the interactions between multiple solar systems are generally limited to rare and transient events, such as star clusters or gravitational encounters. And we are aware of star systems where multiple stars revolve around each other but not of multiple solar systems revolving around a single star.
This question really gets into what it means for one thing to orbit another. Technically, the sun and Jupiter orbit a common center of gravity just a bit outside the body of the Sun. But if you got far enough away and watched the orbit sped up, the sun would be a tiny spot that barely seemed to move, and you would be comfortable saying Jupiter goes around the sun.
To get a nice hierarchical solar system, you would want the main star to be much more massive than the other stars. It's a judgement call just how much more massive it has to be. The sun is 1000 times as massive as Jupiter, but I think you would still say a star has a dominant position if it were only 100 times as massive as the other stars. A pretty small red dwarf has about a tenth the mass of the sun, and there are plenty of stars with ten times the mass of our sun. So, for a few million years, one of those massive stars could be the central star of such a system.
Alas, a few million, or at most a few hundred million, years is as long as such large stars last, so such a system would not last.
If you're happy accepting a 10-to-1 ratio, then you could put two or three red dwarfs, each with its own planets, around a star like the sun. They have to be pretty spread out, with really long orbits, so the different stars don't disrupt the orbits of each others' planets. And that means they ahve to be pretty far from other stars, just so the other stars won't disrupt the overall system. But all of that is possible and might actually happen in real life.
If you are fine with the larger stars in the system co-dominating, then, as another answer points out, the Alpha Centauri system is exactly what you're looking for, right on our doorstep.
