Add query string variables to all hyperlinks URL matching a specified domain

Sorry I read your question wrong. You probably want to use WP_Rewrite and do something like:

add_filter( 'rewrite_rules_array','my_insert_rewrite_rules' );
add_filter( 'query_vars','my_insert_query_vars' );
add_action( 'wp_loaded','my_flush_rules' );

// flush_rules() if our rules are not yet included
function my_flush_rules(){
    $rules = get_option( 'rewrite_rules' );

    if ( ! isset( $rules['(argument_1=test&argument_2=test2)$'] ) ) {
        global $wp_rewrite;
        $wp_rewrite->flush_rules();
    }
}

// Adding a new rule
function my_insert_rewrite_rules( $rules )
{
    $newrules = array();
    $newrules['(argument_1=test&argument_2=test2)$'] = 'index.php?argument_1=$matches[1]&argument_2=$matches[2]';
    return $newrules + $rules;
}

// Adding the id var so that WP recognizes it
function my_insert_query_vars( $vars )
{
    array_push($vars, 'id');
    return $vars;
}

this is untested and mostly stright from the docs but should get you on the right track.