In a two body problem under central force, corresponding to a potential $V(r)$(assume one body is massive compared to the other so that its motion is negligible), conservation of angular momentum implies the motion of the body to be in a plane spanned by position r and momentum p vectors.
But if we have three bodies, one of them massive, are the motions of other two bodies still restricted to a plane? Now the total angular momentum is
$$L = L_1 + L_2 = r_1 \times p_1 + r_2 \times p_2$$
, which is conserved. Mathematically, $L$ could be kept constant while $L_1$ and $L_2$ are changing. Which means we could have motions of the two bodies in two planes at angle to each other, a non-planar motion. Is this allowed in principle? in reality? If not, why? Then, what is reason for the planar motion?