I'm setting up a new store using 1.4.1

I'm trying sort the products in the list by the subcategories they belong to. At the top of list.phtml is

$_productCollection=$this->getLoadedProductCollection();

I tried adding sort filters to that by adding the line

$_productCollection->setOrder('category_ids', 'asc')->setOrder('name', 'asc');

I also tried addAttributeToSort instead of setOrder. This doesn't seem to have any effect. I'm guessing that $_productCollection is not a model I can sort in this manner. I have been digging around trying to find the correct place to apply the sort method without any success.

Can someone tell me the proper place to do this?