Government business tends to be focused on one or two items per sitting. You could select, by some kind of arrangement with the government and the opposition parties, to allow for a third debate to take place that would create more opportunities for the members to participate and express their views on a bill that has already been initiated in the House and can now be discussed further in the parallel chamber while you're still discussing other government items in the main chamber.
It's not impossible to do. In fact, it might be regarded as a beneficial purpose of having the parallel chamber.