Hey Max,
I too had the same question a few weeks ago and can confirm that currently the same field cannot be used in more than one Two-Way Distinct Field Entity Relationship.
With the context you’ve provided, I think the best way to proceed for your particular case would probably be to set up 3 Two-Way Shared Field Entity Relationships. These would be:
Linked Services-Locations
Linked Services-People
Linked Locations-People
Best,
Stanley