  We study a one-dimensional model with F interacting families of Calogero-type
particles. The model includes harmonic, two-body and three-body interactions.
We emphasize the universal SU(1,1) structure of the model. We show how SU(1,1)
generators for the whole system are composed of SU(1,1) generators of arbitrary
subsystems. We find the exact eigenenergies corresponding to a class of the
exact eigenstates of the F-family model. By imposing the conditions for the
absence of the three-body interaction, we find certain relations between the
coupling constants. Finally, we establish some relations of equivalence between
two systems containing F families of Calogero-type particles.
