  We continue the research initiated in hep-th/0607215 and apply our method of
conformal automorphisms to generate various N=4 superconformal quantum
many-body systems on the real line from a set of decoupled particles extended
by fermionic degrees of freedom. The su(1,1|2) invariant models are governed by
two scalar potentials obeying a system of nonlinear partial differential
equations which generalizes the Witten-Dijkgraaf-Verlinde-Verlinde equations.
As an application, the N=4 superconformal extension of the three-particle
(A-type) Calogero model generates a unique G_2-type Hamiltonian featuring
three-body interactions. We fully analyze the N=4 superconformal three- and
four-particle models based on the root systems of A_1 + G_2 and F_4,
respectively. Beyond Wyllard's solutions we find a list of new models, whose
translational non-invariance of the center-of-mass motion fails to decouple and
extends even to the relative particle motion.
