We study the effect of quantum fluctuations on the multiphase point of the Heisenberg model with first- and second-neighbor competing interactions and strong uniaxial spin anisotropy D. By studying the structure of perturbation theory we show that the multiphase degeneracy which exists for S=∞ (i.e., for the axial next-nearest-neighbor Ising model) is lifted and that the effect of quantum fluctuations is to stabilize a sequence of phases of wavelength 4,6,8, . . . . This sequence is probably an infinite one. We also show that quantum fluctuations can mediate an infinite sequence of layering transitions through which an interface can unbind from a wall.