Both the approved RPGs, the Firefly board game, as well as the QMX maps, and the onscreen maps in both Firefly and Serenity, all show a multiple star system.
The official size (as evidenced in The 'Verse In Numbers (TVIN, which is the data derived from the QMX maps and approved by Universal), star orbits are shown to 180 AU distance (1497 LM, or 24.95 light hours). For comparison, Pluto varies between 29.6 and 48.8 AU distance. Sedna is calculated to run between 76 and 937 AU. So, bodies we know to be gravitationally bound can reach further than the distances cited in the official and semi-offical sources.
Note that with the other stars all orbiting White Star (a white star, which, even if a dwarf as is Sol, it would still be more massive than Sol), according to TVIN, two are at opposition at 68 AU (Red Sun and Georgia), then one is at 121 AU (Kalidasa), and the fourth at 180 AU (Blue Sun). So, despite being 5 stars and their planets, they are in fact within gravitational reach of the central star (and would be even if it weren't inherently significantly more massive than Sol), so it's correct to refer to this as a single system.