Membership for Group of people. One payer
If you are using Drupal CMS than you can do this by using webform and webform civicrm module and probably CiviRules. You will need to create 2 membership type Member and Additional member. Setup webform to accept # of contacts with 1st contact as set to use Member membership type and rest of the contact set to Additional member membership.

Set up reminder for membership type member to send membership for primary member. 

(Not sure if the same process can be done in wordpress caldera form plugin)