Origihor

select 
t1.*,
t3.name 
from 
product t1
inner join (
	select 
	product_id
	from product_size
	inner join size on id = size_id
	where name in ('S', 'M', 'L')
	group by product_id
	having count(product_id) = 3
) t2 on t2.product_id = t1.id
inner join (
	select 
	product_id 
	,name
	from product_color
	inner join color on id = color_id
	where name = 'black'
) t3 on t3.product_id = t2.product_id

По моему все можно :-) ибо
Я бы делал через subquery (удобно для выборок по разным условиям из составленного "набора" пересечений)

select BSproduct from
  ( -- Список продуктов имеющих черный цвет и малый размер
    select product as BSProduct from
      (
        SELECT  t1.id,  t1.name AS product,  t3.name AS color,  t5.name AS size
          FROM  `product` AS t1
          JOIN `product_color` AS t2 ON t1.id = t2.product_id
          JOIN `color` AS t3 ON t2.color_id = t3.id
          JOIN `product_size` AS t4 ON t1.id = t4.product_id
          JOIN `size` AS t5 ON t4.size_id = t5.id
      ) 
    where color = "black" and size = "S"  
  ) as BlackAndSmallSize, 
  ( -- Список продуктов имеющих черный цвет и средний размер
    select product as BMProduct from
      (
        SELECT  t1.id,  t1.name AS product,  t3.name AS color,  t5.name AS size
          FROM  `product` AS t1
          JOIN `product_color` AS t2 ON t1.id = t2.product_id
          JOIN `color` AS t3 ON t2.color_id = t3.id
          JOIN `product_size` AS t4 ON t1.id = t4.product_id
          JOIN `size` AS t5 ON t4.size_id = t5.id
      ) 
    where color = "black" and size = "M"  
  ) as BlackAndMidSize, 
  ( -- Список продуктов имеющих большой размер
    select product as LProduct from
      (
        SELECT  t1.id,  t1.name AS product,  t3.name AS color,  t5.name AS size
          FROM  `product` AS t1
          JOIN `product_color` AS t2 ON t1.id = t2.product_id
          JOIN `color` AS t3 ON t2.color_id = t3.id
          JOIN `product_size` AS t4 ON t1.id = t4.product_id
          JOIN `size` AS t5 ON t4.size_id = t5.id
      ) 
    where size = "L"  
  ) as LargeSize
where BSProduct=BMProduct and BMProduct=LProduct

Не знаю как насчет MySQL и его форков, в некоторых SQL серверах можно заранее задавать подзапросы типа

(
        SELECT  t1.id,  t1.name AS product,  t3.name AS color,  t5.name AS size
          FROM  `product` AS t1
          JOIN `product_color` AS t2 ON t1.id = t2.product_id
          JOIN `color` AS t3 ON t2.color_id = t3.id
          JOIN `product_size` AS t4 ON t1.id = t4.product_id
          JOIN `size` AS t5 ON t4.size_id = t5.id
      )

с помощью команды WITH - тогда объем текста выборки сократится в разы.