Using the Windows Powershell arcane interface you can issue the following command to Office 365 to allow users to share/edit calendars. The :calendar is the default calendar, if it is a different name, you should be able to use that name instead. This will then put a copy of the calendar in the Calendar area of the recipient’s calendar section and allow them to add events/appointments.
Add-MailboxFolderPermission -Identity email@example.com:calendar -user firstname.lastname@example.org -AccessRights owner
Fill in the italics with your data.