ONE/3 Multiple Stars
CONVENTION: The most massive star will be called A. The second most massive B, the third most massive C and so on.
STEP ONE: Determine the mean separation of the two first stars involved - the AB pair. (1.3.1 below) Then determine the eccentricity (1.3.2), closest separation, furthest separation, and orbital period.
STEP TWO: If there is a third component (C) determine if it orbits A, B or both. Roll 1d10: 1-3=A, 4-6=B, 7-10=AB. Determine mean separation and eccentricity, limiting the possibilities by the original pair. As a rule, multiple stars orbiting each other cannot orbit in such a way as their orbit get within 3 times of the closest separation and furthest separation of another orbit. So, if the AB pair orbit between 3 and 6 AU, the C-star must orbit either star closer than 1 AU when furthest or 18 AU when closest.
STEP THREE: If there is a fourth component (D) and no more, it will form a pair with the "lone" component above on a roll of 1-7 on 1d10. On a roll of 8-9, it will orbit all three stars. On a roll of 10, it will be in close orbit with one of the already paired stars, if possible. Roll 1d10 again, on a roll of 1-7 it orbits the heavier star of the two. Determine mean separation, eccentricity etc as normal. If there is more components, continue to place them and remember that multiple stars seem to favor pairs. A six-star system is likely to be three pairs, thus.
VERY CLOSE STARS:
Sometimes the stars are so close as to be visibly deforming each other, or perhaps even in contact. This can also happen when one of the stars in a binary leaves the main sequence and becomes a giant, and in these cases mass can actually transfer from the giant to the smaller companion. In other very close binaries, so called BY Draconis stars, one or both of the companions is a flare star and this may create a certain periodicity of the variations.
VERY DISTANT STARS:
When the distance between stars grows, the gravitational forces of the galaxy begin to overcome the forces of the binary. Thus very distant binaries are rather rare.
ORBITS OF MULTIPLE STARS:
Unlike planetary orbits in our solar system, binaries are often distinctly eccentric and multiple stars generally orbit in pairs inclined to the main system orbit. (If you get impossible results, such as a star orbiting inside another star's radius: Reroll.)
When one of the stars in a binary is a neutron star (or a black hole), mass transfer can generate intense amounts of X-ray radiation or even gamma radiation. X-rays can also be generated in other types of binaries, but some sort of mass transfer is necessary.