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