I cannot turn off "Add" permissions to Planning Calendar items, nor can I hid the Add button using Page Designer.  According to a response to Case # 14264343, "the main issue lies in the fact that the "Event" and "Appeal Mailing" options within the Add drop down menu (the one we were attempting to hide) is anchored in completely different areas of CRM, so while we could 'turn off' the ability for other users to see the Add drop down menu, it would assuredly affect their ability to utilize these functions elsewhere within CRM."  We only want to prevent Add from the calendar, not from the places it is currently available.