Possible to assign multiple contacts to a Custom Object?

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Hello! We have a need to assign multiple contacts to a custom object we created called “Meetings”. The current way this CO is designed only allows our team to add one contact to one meeting. Instead we would like a one-to-many relationship where the team could add multiple contacts to each meeting, similar to how we can add multiple contacts to each Incident.

I have tried replicating the report from the contacts tab on incidents, but when I click on the “Add Existing” or “Add New” tab it just transfers ownership of that specific meeting. Whereas, we would like the meeting to have multiple contacts with one main contact.