I understand that Groups can only connect to top-level site collections.
Can a Group be connected to more than one site collection at the same time or is it always a one-to-one relationship between a Group and a site?
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An "Office 365 Group" is a (special) Active Directory group plus a Site Collection. This AD group can be used as an ordinary AD group when granting access to other sites. When used this way, they are just an AD group with no special "Office 365 Group" features in that site. I.e. they are managed as ordinary SharePoint users and are directly assigned permissions to a item, or are added to a "classic" SharePoint group. They will not be treated in any special way because they were an "owner" or "member" in the "Office 365 Group".