We study the simplest perturbation of the matrix model for pure gravity susceptible of reaching the k=3 multicritical point in the framework of the stochastic stabilization of 2D quantum gravity. We show the existence of a line of points in the phase diagram with the genuine critical behavior of the k=2 theory. All the points of the critical line, up to the tricritical point, can be approached from a stable phase at the dominant level in 1/N expansion.