BuddyPress.org

You could filter the body class? Something like this:

function add_body_classes( $classes ) {
    if ( bp_is_member() )
        $classes[] = 'this-is-a-member-profile';

    if ( bp_is_my_profile() )
        $classes[] = 'this-is-my-profile';
}
add_filter( 'body_class', 'add_body_classes', 12 );