Notes:

How exactly would that look?
More importantly what does the lingo completely translate to:

Double Triple Bossy Deluxe:
Double Triple = 6 patties, Bossy = all-beef, Deluxe = everything on it.

On a raft:
Toast in place of burger buns.

4×4:
Previous 6 patties x 4 = 24 total patties, with another 24 slices of cheese.

Animal style:
Patties cooked in mustard, 24 layers of everything.

Extra shingles:
Extra toast, 2 per layer, 14 total.

With a shimmy:
Jelly spread on toast.

And a squeeze:
Orange juice to drink.

Light axle grease:
Light butter on the toast.

Make it cry:
Extra onions.

Burn it:
Patties are well-done.

Let it swim:
Extra special sauce.