I'll be honest that I don't really understand the way you've expressed your requirement, however I believe this solution matches the result set you listed.

-- Solution 3: List combinations up to 3

;WITH UNIQUEnTuples (n, Class, Product, Tuples, Product2) AS (

SELECT 1, Class, Product

,CAST(Product AS VARCHAR(MAX)), NULL

FROM @ProductClass

UNION ALL

SELECT 1 + n.n, t.Class, t.Product

,CAST(t.Product AS VARCHAR(MAX)) + '+' + n.Tuples

,n.Product

FROM @ProductClass t

JOIN UNIQUEnTuples n ON CAST(t.Product AS VARCHAR(MAX)) < n.Tuples AND

n.Class <> t.Class

WHERE CHARINDEX(CAST(t.Product AS VARCHAR(MAX)), n.Tuples) = 0 AND n < 3

)

SELECT [Group ID]=CASE n WHEN 3 THEN 1 ELSE 2 END, [Item Group ID]=[Group ID], Product=item

FROM (

SELECT [Group ID]=ROW_NUMBER() OVER (PARTITION BY n ORDER BY Product2, Product)

,[Product Group]=Tuples, n

FROM UNIQUEnTuples

WHERE n IN (2,3)) a

CROSS APPLY dbo.DelimitedSplit8K([Product Group], '+')

ORDER BY CASE n WHEN 3 THEN 1 ELSE 2 END