  A new generalization of the Calogero's rational ($A_N$) many-body quantum
model is proposed and studied. The key innovation lies in an asymmetrization of
the Calogero's two-body interaction. In the generalized model the exact
solvability is preserved while the Calogeero's single coupling constant $C$ is
replaced by a certain multiplet of freely variable parameters. The resulting
Calogero-like Hamiltonian ceases to be re-arrangement-invariant. As a
consequence, the degeneracy of the bound-state spectrum gets partially
unfolded.
