I've made some custom systems during my time using SE, so I thought I'd dump them here. Can't guarantee they're amazing, though.
Here you'll find addons based on other things, like books and video games.
Ga'Hoole Sol system v1 (Warning: may not work properly)
Thousands of years in the future, humanity has relocated to a terraformed Venus. As they spread across the solar system, adjusting its worlds to their desire, Earth, whose oceans have moved far inland, is left untouched. Inspired in part by Guardians of Ga'Hoole by Kathryn Lasky.
Trinity system v1
400 light-years from Earth is the Trinity system, a triple star system with many habitable worlds, namely the gas giant Hyperion and its moons, three of which are home to intelligent life. Based on Seed of Andromeda by Regrowth Studios.
AcceleRacers worlds v1
A more silly addon, this mod attempts to recreate the realms seen in the kids' movie series AcceleRacers. Contained is a solar system positioned in NGC 5377 with many planets and moons.
These are systems I've made for the 100th Millennium wiki, which uses Space Engine to create a massive future history. You can check it out here.
Eya system v1
Located at the edge of the Omega Centauri cluster, Eya is a human-inhabited system home to Brayleigh, the capital world of the Centauri Confederacy. This system only contains Brayleigh, so I might add more to it later.
Canisteo system v1
Despite its great distance from most of human space, Canisteo is a major system of the Confederacy of Humanity. Its most populated planet, Agsia, was terraformed and inhabited with the purpose of providing food for other colonies.
Nortesx system v1
One of humanity's earilest alien contacts were the inhabitants of the Nortesx system. This binary system consists of a yellow dwarf and an orange dwarf. Currently only has the planet has Daylie.
Circini system v1
Circini was the first system in the Circinus galaxy humans accessed via wormhole. Millennia later it remains the capital system of the influential Circinus Republic.
Aryabhata system v1
Located in the Aryabhata system is Tkowes, a chilly but temperate Earth-like planet home to a young spacefaring civilization of the same name. It was during this youth the Tkowes and humans first interacted, and the two have been close allies since.