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In this paper we present a detailed study of the antiferromagnetic classicalHeisenberg model on a bilayer honeycomb lattice in a highly frustrated regimein presence of a magnetic field. This study shows strong evidence of entropicorder-by-disorder selection in different sectors of the magnetization curve.For antiferromagnetic couplings $J_1=J_x=J_p/3$, we find that at lowtemperatures there are two different regions in the magnetization curveselected by this mechanism with different number of soft and zero modes. Theseregions present broken $Z_2$ symmetry and are separated by a not fullycollinear classical plateau at $M=1/2$. At higher temperatures, there is acrossover from the conventional paramagnet to a cooperative magnet. Finally, wealso discuss the low temperature behavior of the system for a less frustratedregion, $J_1=J_x<J_p/3$.

Field induced multiple order-by-disorder state selection in antiferromagnetic honeycomb bilayer lattice