Squeezing as much liquid as possible out of a stock: a practical approach?
Not difficult at all if you truly want to get every possible last drop. Choose a large clean tea towel for this purpose only. After you've drained most of the liquids out, line your colander with the tea towel and pour the last bit with meat and vegetables in. I found using clothespins to the towel in place is best. Gather the corners up and you can either use a heavy thick elastic to secure the contents into a bagged ball or use heavy twine tied around it. I prefer twine. Less risk of breaking and you've got a long end to hang the ball. 

I've done similar but not with soup stock as I always use meat with bones. If you tie one end of the twine up (on a cupboard door handle, for instance),you can put a bowl under it to catch the stock. Start at the top of the ball so when you squeeze, ut runs down lower. Work your way to the bottom. I doubt you'll be able to extract much more after that.

Make sure you scrape the remains off the tea towel right afterward and rinse off any bits left on. Then rinse well and include in the laundry. Otherwise, it's just about impossible to clean later. I know as I got busy with other things and forgot.