  We study a hierarchy of directed percolation (DP) processes for particle
species A, B, ..., unidirectionally coupled via the reactions A -> B, ... When
the DP critical points at all levels coincide, multicritical behavior emerges,
with density exponents \beta^{(k)} which are markedly reduced at each hierarchy
level k >= 2. We compute the fluctuation corrections to \beta^{(2)} to
O(\epsilon = 4-d) using field-theoretic renormalization group techniques. Monte
Carlo simulations are employed to determine the new exponents in dimensions d
<= 3.
