I have a slight rewrite that works. might not be better than any thing else but will eat as many sets with as many items in the set as you want to feed it(Of course you will need to modify the cross apply to include more columns).

IF OBJECT_ID('tempdb..#Tmp') IS NOT NULL DROP TABLE #Tmp

--The temp table makes things a little easier

SELECT * INTO #Tmp

FROM (select 1 I, '1' D1, '1' D2, '1' D3 union

select 2 I, '1' D1, '1' D2, '2' D3 union

select 3 I, '1' D1, '2' D2, '3' D3 union

SELECT 4,'A','A','A' UNION

SELECT 5,'B','A','A')X

DECLARE @T AS GenericTable

--Normalize the data so it plays nicely with our iTVF

INSERT INTO @T

SELECT I, Value

FROM #Tmp

CROSS APPLY (VALUES (D1),(D2),(D3))X(Value)

SELECT *

FROM AreEqual (@T) a

INNER JOIN #Tmp b

ON a.ID = b.I

It is still a 2 step process but now we can load as many sets as we want into the table valued parameter and get our proper results.

EDIT: This is also for me to play with a couple of things and get more experience with them. so it may not be fast or work in your situation but does use some things i have been studying.