Hook into other module's field formatter?
The question mentions that hook_field_formatter_view() is only called on the originating module, but you can take ownership of the field formatter via hook_field_formatter_info_alter().

You should be able to set the module key of the formatter to MYMODULE like:

function MYMODULE_field_formatter_info_alter(&amp;$info) {
  $info['some_field_formatter']['module'] = 'MYMODULE';
}


Then you can implement MYMODULE_field_formatter_view(), optionally feeding through the existing module which handled it to get an element to alter.

function MYMODULE_field_formatter_view($entity_type, $entity, $field, $instance, $langcode, $items, $display) {
  // Your custom logic
  $element = OTHER_field_formatter_view($entity_type, $entity, $field, $instance, $langcode, $items, $display);
  // Any alterations
}