When you are on the Products page, you will be able to create a New Assortment, Save All Products to your current assortment, or Select Saved Assortments on the left hand side of the page.
When you select Saved Assortments, you will be able to view My Assortments, and also all Shared Assortments.
You will now be able to select any of your assortments under the My Assortment tab.
Note: the orange star shows you what assortment has been selected as the Default Assortment.
When you select the Others tab, you will now be able to choose any of the assortments that you have permission to view.
You also can utilize the Search bar on the top right to search for a specific Assortment.
Once you find the assortment that you are looking for, you are now able to assign that assortment as your Default Assortment on the Product page.
Now on the Products page, you have the shared assortment selected as your Default Assortment and you are able to add products to this assortment. As long as you have permission to the assortment, you are now able to not only remove, but to add products to assortments.