Technically - if you pop up the signs menu, hit select (to move to another UI component), circle to deselect, you can then move the soft targeting cursor to the next object, hit select to focus onto the signs menu again, and place the next mark.

Also - you can hold either L2 or R2 and use the L1 (shift target left) and R1 (shift target right) buttons to change your anchor target (obviously only on enemies), which will also let you quickly shift from enemy to enemy to mark them. This solution is of note as your suggestion would break this functionality and make it the overly complicated method, while it is technically what you are requesting with the exception of it being automatic.

Using soft target to mark would probably be best suited to cross hotbar shortcuts for optimal speed (and this is possible).