It has been a while...
It would seem that Lamarque elucidated exactly what MacDonald himself stated, that the final compound evolution would have the battalions deployed eventually doubled.
There are two means in the system to double a line, one is to double by sections so that three ranks become six ranks, or have another line marching behind at a should distance to eventually double the depth of the first line to six ranks as well. This now gave order of depth and strength to defend against cavalry. It is for that reason the French system used colonnes serrees et de la ligne deployee (lines doubled to six ranks).
I hope this helps