Often all that is needed is to change something like this
require_once 'include/SugarEmailAddress/SugarEmailAddress.php';
to
require_once get_custom_file_if_exists('include/SugarEmailAddress/SugarEmailAddress.php');
However, that is only one of the mechanisms SuiteCRM has for customization, and not the best one.
Since SugarEmailAddress is an object, and a core Bean, I suppose it can be extended in an upgrade-safe manner with the Extension mechanism, see modules.ext.php