  As a generalization and extension of JMP 54 (2013) 022901, the classical
dynamics of three non-relativistic Coulomb charges $(e_1, m_1)$, $(e_2, m_2)$
and $(e_3, m_3)$ on the plane placed in a constant magnetic field perpendicular
to the plane is considered. Special trajectories for which the distances
between the charges remain unchanged are presented and their corresponding
integrals of motion are indicated. For these special trajectories the number of
integrals of motion is larger than the dimension of the configuration space and
hence they can be called \emph{particularly superintegrable}. Three physically
relevant cases are analyzed in detail, namely that of three electrons, a
neutral system and a Helium-like system. The $n$-body case is discussed as
well.
