You can't open and then save to the file. It doesn't work that way. You have to download the file, edit it and then save it so this isn't such a good idea to share calendars.
Did you check horde caledar?
Kronolith
The Kronolith calendar provides a robust web-based calendar for any number of users or groups, with the ability to show any number of calendars in a single overlaid view. Users can create any number of calendars and grant read, edit, or full permissions to any user, group, or any combination thereof.