Actauly I know differently,
Assuming you get the peltier into a state whereby you dont actualy create a hot side, (as its well heatsinked) you then create a condition where the othr modules run much more efficently.
As you correcly said, the devices pump the heat from one module to the other. The result will be of course the need for a very big heatsink and possibly a radiator of sorts on the hotside, to remove the heat, but the cooling power of the combined units will be astronimoical. I have made one in the past using copper blocks between modules, and had the hot side mounted to a 1" thickk 500mmx500mm slab of aluminum as a heatsink. It generated a lot of ice, hovewer i have no pictures of it in action, however il be making a new one very soon when my 10x 138W modules come in the post.
I think if you have tried and failed the above technique, you probaly should consider machining your own heatsinks, unless you already have... the goal in any peltier system, get the hot side as cold as you can, and the cold side will get bloddy cold.
hope this helps.