  We constructed the most general N=4 superconformal 3-particles systems with
translation invariance. In the basis with decoupled center of mass the
supercharges and Hamiltonian possess one arbitrary function which defines all
potential terms. We have shown that with the proper choice of this function one
may describe the standard, $A_2$ Calogero model as well as $BC_2, B_2,C_2$ and
$D_2$ Calogero models with N=4 superconformal symmetry. The main property of
all these systems is that even with the coupling constant equal to zero they
still contain nontrivial interactions in the fermionic sector. In other words,
there are infinitely many non equivalent N=4 supersymmetric extensions of the
free action depending on one arbitrary function. We also considered
quantization and explicitly showed how the supercharges and Hamiltonian are
modified.
