After entering the personal details of the invitee, under 'additional guests allowed' you can select whether you want the person to be able to bring an unlimited number of guests or up to a certain number. Unlimited means your guest is able to bring however many persons they want, up to X means they can bring a limited number of people. The limit is set by the event's host. If no additional guests are allowed, your invitee won't be able to enter other names while RSVPing.
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If your event has a large number of invitees, instead of manually adding every single one of them, you can import your invite list and have the process done in just a few clicks. Before importing, edit the details of your Excel spreadsheet. The F column is the one reserved for the additional guest(s) allowed. Simply type in the number of +1s allowed for every guest and leave blank or enter 0 if the event is invite-only. Type 'Unlimited' if your guest can bring as many guests as they want.

Don't forget that even after you import your invite list if you change your mind and want to enable/disable someone from bringing +1's you can do this under Invite List > Invitees. Simply click on the invitee, update the details and click Save & Close.