Icons to "create new cart" and "add items to cart"

For an app where it is possible to have multiple shopping carts (like an aggregator), I am considering icons for making a new cart and for adding items to cart.

Does it make sense to use the cart icon with the plus for creating a new cart and the cart icon with the down arrow for adding a new item to the cart? Could the cart icon with down arrow be (mis)understood as something else?

Then correspondingly, does it make sense to use cart icon with up arrow to remove items from the cart, and the cart icon with minus or cross sign to remove the whole cart?

Or is it too ambiguous?

Addition 1: The buttons contain the icon with a short text.

Addition 2: This other question has very good discussion on using icons only vs. icons + text vs. text only. It seems there is some research that indicated icons + text works best in many cases.