Drupal - How can I set the value of a taxonomy term reference to multiple terms using PHP?

Assuming the field is set up to accept multiple records...

$user->field_yourfield_name[LANGUAGE_NONE][0]['tid'] = 27;
$user->field_yourfield_name[LANGUAGE_NONE][1]['tid'] = 28;
// etc

Or you can just keep appending to the array (without knowing the next available index) like this:

$user->field_yourfield_name[LANGUAGE_NONE][]['tid'] = 27;
$user->field_yourfield_name[LANGUAGE_NONE][]['tid'] = 28;