OK, this is interesting, yuo may be right. I found this on Wiki... granted not the best source somedays, but it fits what your saying:
During the short television run of the Firefly series, it was not made clear whether the planets and moons depicted were located in one planetary system or many (however, creator Joss Whedon, as well as all licensed products, confirms that there is no faster-than-light travel in the Firefly universe)[1]. The opening narration of the film makes it clear that the planets and moons are in one system with "dozens of planets and hundreds of moons." This is supported by production documents published in Serenity: The Official Visual Companion.In 2008, a double sided poster called the Complete and Official Map of the Verse was produced, which depicts the system as consisting of one central star (the "White Sun") orbited by the "core worlds" and several other stars (each of which has its own planetary system).
But then there is this in the same article:
According to The Complete and Official Map of The Verse, the Verse is also known as 34 Tauri (2020), although it should be noted that the real 34 Tauri is not a star, but an object accidentally cataloged as a star by astronomer John Flamsteed in 1690 which was later determined to be the planet Uranus. A pdf The Verse in Numbers that accompanies the map on its official website, and from which the map is based, states that in 2020 Earth astronomers discover that 34 Tauri, up until that time was thought to be a single star, was actually a cluster of five stars and several brown dwarfs, and soon numerous Earth-sized planetary bodies are discovered. Plans to colonize the system were underway by the 22nd century when conditions on Earth become so bad that it can no longer support human life and humanity needed to find a new home. Terraforming technology, (tested on Earth's moon Luna and the planet Mars), was eventually developed to a level capable of increasing the surface gravity of a moon-sized body to around 1G (Earth standard) and hold surface water and atmosphere necessary to sustain life.
The system has five stars and seven brown dwarf/protostars. All the stars orbit the White Sun, (also called 34 Tauri (2020) A, or Bai Hu (White Tiger) by the Chinese), which is a class A0 giant, 2.5 times bigger than Sol and 80 times as bright. The "Central Planets" are the terrestrial worlds that orbit the White Sun. Farther out in this system the Red Sun (a class G5, also called 34 Tauri (2020) B, or Zhu Que (Red Phoenix)) and Georgia (class G0, also called 34 Tauri (2020) C, Huang Long (Yellow Dragon)) share an orbit and worlds orbiting these stars are referred to as "Border Planets". The fourth star Kalidasa (class F5, also called 34 Tauri (2020) D, or Xuan Wu (Black Tortoise)), and its planets orbit next. After that, the fifth and last star Blue Sun, (class F0, also called 34 Tauri (2020) E, or Qing Long (Blue Dragon)), and its planets orbit. Worlds orbiting these last two stars comprise "The Rim". Planets too far away from the biozones of the main stars are sustained for habitability by a series of protostars. The protostars Qin Shi Huang and Lux orbit the White Sun. Murphy orbits Georgia. Himmbjørg and Heinlein orbit the Red Sun, Penglai orbits Kalidasa, and Burnham orbits the Blue Sun.
The number of terraformed worlds in the system is never mentioned in the series though in a deleted scene from the episode "Our Mrs. Reynolds", Captain Malcolm Reynolds mentions to the character Saffron that there are "more than 70 earths spinning in this galaxy and the meek have inherited not a one." However, the opening narration of the film Serenity gives us a brief history of the Firefly universe and mentions; "Earth that was could no longer sustain our numbers, we were so many. We found a new Solar system, dozens of planets and hundreds of moons."
All of the following bodies were terraformed and made to have a standard atmosphere and gravity in order to be capable of supporting human life. During the movie Serenity, the planet Miranda is speculated to be a "black rock" – a planet where no life exists or is possible. A generic explanation (that the terraforming did not hold) is offered to explain it, indicating that this simply happened some times while the terraforming process was occurring.
There is also a great list of the worlds mentioned on Firefly, but I'm not gonna fill another 2 pages with it...lol.
Sins Forums
It would be possible of course to have a small mod created where just a tech frigate class light ship would be considered "Serenity" and to give them perhaps the pirate stealresources ability, and heavy hull points and moderate shields and to link them with an ally race so they dont have to have a homeworld. 
