By using a Monte Carlo simulation, we have studied the effects on the multilayer transition and magnetic properties of the crystal field D ∕ J 2 , the four-spin coupling J 4 ∕ J 2 and RKKY interaction in the spin-1 Ashkin–Teller (AT) model of a system composed of two magnetic multi-layer materials, of various thicknesses, separated by a nonmagnetic spacer of thickness M. By varying the strength of J 4 ∕ J 2 , we have obtained a new partially ordered phase 〈 σ S 〉 , for different values of D ∕ J 2 . We have established a rich phase diagram with first and second-order phase transitions with tricritical points. It is shown that the transition temperature of both magnetic blocks depends strongly on the thickness of the magnetic layers N , as well as J 4 ∕ J 2 and D ∕ J 2 . There exists a critical thickness of the magnetic layers N L above which the multilayer blocks undergo a transition separately at different temperatures, for a high value of J 4 ∕ J 2 and D ∕ J 2 . Besides, the critical exponents are computed. [ABSTRACT FROM AUTHOR]