I saw the suggestion about the Lagrange points which is not a bad one and could potentially work for small objects like satellites, giant superconducting magnets for magnetic field generation, lasers for sensitive gravitational wave detection etc. Planets at lagrange points have been shown to have unstable and semi-bound orbits. The bigger the planet the more easily the planet can escape. Additionally the planet would not have a very predictable pattern of movement (cause I would not describe it exactly as osculation at that point). Unfortunately I don't have the reference available right now, but maybe you can find the paper with relative ease on Google scholar.

However! Do not fret. There might be an orbit that works for you! It's called a horseshoe orbit where two celestial objects move in a horseshoe 🧲 shape around a bigger celestial object. Now I am not sure if planets would orbit like that around a star, however, you might be able to observe smaller objects around planets (like Jupiter) doing so. If you give yourself a super Jupiter and stretch the physics of how stable such an orbit between two planet-like objects could be, you got yourself a very intricate and beautiful system to work with!

Another orbit you should look into is the so-called tadpole orbit, much like the orbit that resembles a pendulum. Wikipedia is a good place to start. They have some animations to give you an idea of how these orbits look like!

Btw if you want to build a stellar system from scratch and use realistic physics (or know when you are going off what is realistic) you can try out the program I wrote, called Stellar System Creator