  We revisit the (untwisted) superfield approach to one-dimensional
multi-particle systems with N=4 superconformal invariance. The requirement of a
standard (flat) bosonic kinetic energy implies the existence of inertial
(super-)coordinates, which is nontrivial beyond three particles. We formulate
the corresponding integrability conditions, whose solution directly yields the
superpotential, the two prepotentials and the bosonic potential. The structure
equations for the two prepotentials, including the WDVV equation, follow
automatically. The general solution for translation-invariant three-particle
models is presented and illustrated with examples. For the four-particle case,
we take advantage of known WDVV solutions to construct a D_3 and a B_3 model,
thus overcoming a previously-found barrier regarding the bosonic potential. The
general solution and classification remain a challenge.
