Add extra custom permissions to Field Permissions
With Drupal 8, the module implemented the permission type plugins. To add more permissions, you implement a new permission type plugin, using one of the existing plugin classes as example, such as Drupal\field_permissions\Plugin\FieldPermissionType\CustomAccess or Drupal\field_permissions\Plugin\FieldPermissionType\PrivateAccess.  Drupal\field_permissions\Plugin\FieldPermissionType\Base is used as base class, and simplifies the creation of new permission type plugins.
Note that the module invokes the hook_field_permission_type_plugin_alter() implementations, as described in the field_permissions.api.php file. That hook can just be used to remove a permission type plugin, or change the plugin properties given in its annotation (which doesn't include the permissions exposed from the plugin, for what I can see).