This paper studies a variant of the container loading problem in which to the classical geometric constraints of packing problems we add other conditions appearing in practical problems, the multi-drop constraints. When adding multi-drop constraints, we demand that the relevant boxes must be available, without rearranging others, when each drop-off point is reached. We present first a review of the different types of multi-drop constraints that appear in literature. Then we propose a GRASP algorithm that solves the different types of multi-drop constraints and also includes other types of realistic constraints such as full support of the boxes and load bearing strength. The computational results validate the proposed algorithm, which outperforms the existing procedures dealing with multi-drop conditions and is also able to obtain good results for more standard versions of the container loading problem.