¿Cómo puedo ordenar filas seleccionadas alternativamente?

Intente esta consulta a continuación. Usando ROW_NUMBER() OVER(PARTITION BY ..) generar un rango/número de registro para cada 'which' elementos y ordenar en base a esto. (Espero que esto funcione para usted, no tengo el esquema de tabla o el script de datos de muestra para probarlo yo mismo)

SELECT
  pr1.id AS user_id,
  pr1.title AS user_name,
  pr2.id AS liker_id,
  pr2.title AS liker_name,
  x.which AS which_table,
  x.cnt AS total
FROM 
(
  SELECT rid, rootid, which, COUNT(*) AS cnt
        ,ROW_NUMBER() OVER(PARTITION  BY which ORDER BY rid) AS new_order
  FROM
  (
    SELECT rid, rootid, 'vote' which FROM p_likes
    UNION ALL 
    SELECT rid, rootid, 'comment' which FROM p_comments
    UNION ALL 
    SELECT rid, rootid, 'friend' which FROM relations
  ) y
  WHERE y.rootid = 1246 AND y.rootid <> y.rid
  GROUP BY y.rid, y.rootid, y.which
) x
INNER JOIN pagesroot pr1 on x.rootid = pr1.id
INNER JOIN pagesroot pr2 on x.rid = pr2.id
ORDER BY new_order,x.cnt desc;