Do you know how many 'Team Template' can be created per entity by default ? CRM 2013 by default allows you to create only 2 'Team Template' per entity. When you try to create more than 2 access team template for any particular entity, it prevents user from creation it with error message "There are too many team templates for this entity. Delete an existing team template, and then try again.".
A maximum number of templates that you can create for an entity is specified in deployment setting (MaxAutoCreatedAccessTeamsPerEntity). The default value is 2.