The Dagwood is defined by a single excess: it is built taller than a sandwich can structurally be, on purpose. Where the club solved the BLT's instability by adding one bracing slice of toast, the Dagwood runs the opposite way, stacking layer on layer of cold cuts, cheeses, vegetables, condiments, and sometimes whole pickles until the thing is taller than it is wide and can only be held together with a long skewer through the top. The height is not a side effect of generosity. It is the entire identity. A Dagwood that could be eaten in a normal bite would not be a Dagwood.
It works, to the extent it works, as a deliberate engineering joke that still has to obey physics at the lunch counter. The skewer is load-bearing, the only thing keeping the tower vertical, and the build order matters more here than in any sane sandwich: heavier, flatter layers low, the slippery and the wet, tomato, dressing, kept off the bottom slice so the base does not give before the structure is even finished. The bread has to be sturdy enough to anchor the skewer without tearing, because the slice at the bottom carries the compressed weight of everything above it. In practice the sandwich is built to be admired and then disassembled or compressed to a bitable height before anyone eats it, which is the honest reality of the form: the spectacle is half the point and the kitchen knows it.
The variations are a question of how far to push the stack. The restrained reading is just an overbuilt club, three or four fillings braced with a middle slice. The maximal reading treats the height as a dare. Each of those deserves its own article rather than being crowded in here.