Alright.  I may be going around the barn to get to the horse, (or however the saying goes), but this seems to work.  Hopefully, someone will figure out a more elegant and streamline method. 

CREATE TABLE #u_external_requests( acct_number int,

                                                           idx int,

                                                           stage int)

INSERT INTO #u_external_requests VALUES( 1000000179, 1, 7)

INSERT INTO #u_external_requests VALUES( 1000000179, 2, 1)

INSERT INTO #u_external_requests VALUES( 1000000192, 1, 7)

INSERT INTO #u_external_requests VALUES( 1000000192, 4, 8)

INSERT INTO #u_external_requests VALUES( 1000000192, 5, 1)

INSERT INTO #u_external_requests VALUES( 1000000192, 6, 8)

INSERT INTO #u_external_requests VALUES( 1000000205, 1, 8)

INSERT INTO #u_external_requests VALUES( 1000000205, 5, 7)

INSERT INTO #u_external_requests VALUES( 1000000689, 1, 8)

INSERT INTO #u_external_requests VALUES( 1000000689, 3, 7)

INSERT INTO #u_external_requests VALUES( 1000000689, 4, 8)

INSERT INTO #u_external_requests VALUES( 1000000705, 1, 7) -- Test values for only one entry....

CREATE TABLE #OutPut( acct_number int,

                                       idx int,

                                       stage int)

DECLARE @CurrentAcctNum int,

                 @MaxAcctNum int

SELECT @CurrentAcctNum = (SELECT MIN( acct_number) FROM #u_external_requests)

SELECT @MaxAcctNum = (SELECT MAX( acct_number) FROM #u_external_requests)

WHILE @CurrentAcctNum <= @MaxAcctNum

BEGIN

            INSERT INTO #OutPut

            SELECT TOP 2 acct_number, idx, stage

            FROM #u_external_requests

            WHERE acct_number = @CurrentAcctNum

            SELECT @CurrentAcctNum = (SELECT MIN( acct_number)

                                                          FROM #u_external_requests

                                                          WHERE acct_number > @CurrentAcctNum)

END

SELECT acct_number, idx, stage

FROM #OutPut

DROP TABLE #OutPut

DROP TABLE #u_external_requests