Untested (and can't test right now) but you ought to be able to add attributes with a filter... something like:
function test_sc($atts,$content) {
// echo 'test_sc';
$atts = shortcode_atts(
array(
'foo' => 'no foo',
'bar' => 'default bar',
),
$atts,
'testsc'
);
// var_dump($atts);
}
add_shortcode('testsc','test_sc');
function test_shortcode_att_add($atts) {
# this filter should only run once (first use on page)
remove_filter('shortcode_atts_testsc','test_shortcode_att_add');
$atts['xxx'] = 'yyy';
return $atts;
}
add_filter('shortcode_atts_testsc','test_shortcode_att_add');
Of course, I don't know exactly what you attribute you are trying to add, or what kind of supporting code it might depend on.