  We study multifield extensions of Reggeon Field Theory (also equivalent to
Directed Percolation model) at criticality in the perturbative
epsilon-expansion below the upper critical dimension Dc=4 at one loop, for the
special case when all fields have the same scale (anomalous) dimensions.
Analyzing all the fixed points of the renormalization group flow for N=2
flavors and some for N=3, we find scale invariant solutions which are
characterized by specific emergent global symmetries of the interacting
potential. We also study two infinite families as a function of N having Z_N
and S_{N+1} symmetries.
