  Phase transitions of the 2A-> 3A, 4A->0 reaction-diffusion model is explored
by dynamical, N-cluster approximations and by simulations.The model exhibits
site occupation restriction and explicit diffusion of isolated particles. While
the site mean-field approximation shows a single transition at zero branching
rate introduced in PRE {\bf 67}, 016111 (2003), N>2 cluster approximations
predict the appearance of another (reentrant) transition line for weak
diffusion (D). This latter phase transition is continuous, occurs at finite
branching rate and exhibits different scaling behavior. I show that the
universal behavior of this transition is in agreement with that of the PCPD
model both on the mean-field level and in one dimension. Therefore this model
exhibiting annihilation by quadruplets does not fit in the recently suggested
classification of universality classes of absorbing state transitions in one
dimension (PRL {\bf 90}, 125701 (2003)). For high diffusion rates the effective
2A->3A->4A->0 reaction becomes irrelevant and the model exhibits a mean-field
transition only. The two regions are separated by a non-trivial critical
endpoint at D*.
