You could, but you'd all have to share the same iCloud account and hence a single Apple ID, at least for that. You might want to look into Google Calendar which allows you to share calendars and sync them to your iOS device.
Someone else here might have other suggestions.
From the User Guide.
“Share iCloud calendars
You can share an iCloud calendar with other iCloud users.”
“When you share a calendar, others can see it, and you can let them add or change events. You can also share a read-only version that anyone can view.
Create an iCloud calendar. Tap Calendars, tap Edit, then tap Add Calendar in the iCloud section.
Share an iCloud calendar. Tap Calendars, tap Edit, then tap the iCloud calendar you want to share. Tap Add Person and enter a name, or tap to browse your Contacts. Those you invite receive an email invitation to join the calendar, but they need an iCloud account in order to accept.”
Excerpt From: Inc, Apple. “iPad User Guide For iOS 7.” Apple Inc., 2014. iBooks.
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