Contextual menu with Combobox

Is there a way to pop up a contextual menu while the combobox list is displayed? Essentially what I’m trying to do is to have the list’s highlight track the mouse and let the user bring up a menu of optional operations depending on the item highlighted without that item being selected.

Since in my app, the contents of the combobox’s list is populated dynamically, I want the user to be able to delete an item from the list without it having to be selected.