To thicken soup without flour or cornstarch you can add some coconut milk or soup thickener to the soup.
Also adding some butter or pureed vegetables such a pureed potatoes can add thickness to the soup.
The potatoes contain starch which is a good way to thicken soup and by having the potatoes pureed it increases the thickness of the soup.
To make soup thicker without cornflour you can also use butter and flour paste.
Mix together some flour into a paste with some water and then add butter along with the flour paste.
The butter and flour paste will work just as good as cornflour to thicken your soup.
The butter and flour paste that you use to thicken soup is called beurre manié.
To use the beurre manié to thicken your soup mix 2 tsp flour with 2 tsp soft butter, and while the soup is simmering, stir the paste into the pan.
You can also thicken soup by adding just some flour or some lentils or rice or even cream or Yogurt to the soup a little at a time until it thickens up.
You can also pour the soup through a Sieve to remove some of the excess thinner liquid.