This WHILE LOOP might be a little cleaner and faster than what you've got and should resolve to any number of levels.

DECLARE @increment TINYINT

DECLARE @didinsert TINYINT

/* create test data for person id combinations */

CREATE TABLE #personIds(

partykey INT

,personId INT

)

INSERT INTO #personIds

SELECT 1, 1

UNION ALL

SELECT 2, 3

UNION ALL

SELECT 3, 1

UNION ALL

SELECT 3, 3

UNION ALL

SELECT 4, 4

;

/* create test data for orders */

CREATE TABLE #orders (

orderId INT

,partykey INT

)

INSERT INTO #orders

SELECT8829, 1

UNION ALL

SELECT 9323, 3

UNION ALL

SELECT 7321, 4

;

/* to store all partykey combinations */

CREATE TABLE #orderPartyIds (

orderid INT

,partykey INT

,personid INT

,incrementNbr TINYINT

)

;

DECLARE @RowsCount INT, @Iteration INT = 1;

INSERT INTO #orderPartyIDs (orderid, partykey, personid, incrementNbr)

SELECT orderid, a.partykey, b.personid, @Iteration

FROM #orders a

JOIN #personIDs b ON a.partykey = b.partykey;

SELECT @RowsCount = @@ROWCOUNT, @Iteration = @Iteration + 1;

WHILE @RowsCount > 0

BEGIN

INSERT INTO #orderPartyIDs (orderid, partykey, personid, incrementNbr)

SELECT orderid, partykey, personid, @Iteration

FROM

(

SELECT a.orderid, b.partykey, b.personid

FROM #orderPartyIDs a

JOIN #personIDs b ON a.personid = b.personid OR a.partykey = b.partykey

EXCEPT

SELECT orderid, partykey, personid

FROM #orderPartyIDs

) a;

SELECT @RowsCount = @@ROWCOUNT, @Iteration = @Iteration + 1;

END

SELECT orderid, partykey, IncrementNbr

FROM

(

SELECT orderid, partykey, IncrementNbr

,rn=ROW_NUMBER() OVER (PARTITION BY orderid, partykey ORDER BY IncrementNbr)

FROM #orderPartyIDs

) a

WHERE rn=1;

GO

/* clean up */

DROP TABLE #personIds

DROP TABLE #orders

DROP TABLE #orderPartyIds

Note that I added a column to your #orderPartyIDs temp table.