You can "can" leftover soup.
Using canning jars and a pressure cooker to seal the jars after adding the leftover soup you can "can" the leftover soup and it will last longer that way.
Can you can soup without a pressure canner? No, soups will always need to be pressure canned.
Do not add noodles, rice, flour, cream, or any milk or thickeners.
All of these can be added when you heat the soup to serve it.