I cleaned up your sample data and came up with a not so optimal solution . This can be greatly improved by removing the need for the DISTINCT clause. Using MAX with and OVER clause is also not a great practice. All that said, here's my solution:

USE Tempdb

GO

IF OBJECT_ID('tempdb..HISTORY') IS NOT NULL DROP TABLE HISTORY;

CREATE TABLE HISTORY

(

CUSTOMER VARCHAR(10),

PLANNBR VARCHAR(10),

SUBPLAN VARCHAR(3),

STARTDATE DATE,

ENDDATE DATE,

HISTORYMONTH VARCHAR(6));

GO

INSERT INTO HISTORY(CUSTOMER, PLANNBR, SUBPLAN, STARTDATE, ENDDATE, HISTORYMONTH)

VALUES

('9111111', 'H1111LAC', '006', '2014-01-01', '2014-05-31', '201401')

,('9111111','H1111LAC', '006', '2014-01-01', '2014-05-31', '201402')

,('9111111','H1111LAC', '006', '2014-01-01', '2014-05-31', '201403')

,('9111111','H1111LAC', '006', '2014-01-01', '2014-05-31', '201404')

,('9111111','H1111LAC', '006', '2014-01-01', '2014-05-31', '201405')

,('9111111','H1111OC', '010', '06-01-2014', '2999-12-31', '201406')

,('9111112', 'H1111LAC', '006', '2014-01-01', '2014-05-31', '201401')

,('9111112','H1111LAC', '006', '2014-01-01', '2014-05-31', '201402')

,('9111112','H1111LAC', '006', '2014-01-01', '2014-05-31', '201403')

,('9111112','H1111LAC', '006', '2014-01-01', '2014-05-31', '201404')

,('9111112','H1111LAC', '006', '2014-01-01', '2014-05-31', '201405')

,('9111112','H1111LAC', '018', '06-01-2014', '2999-12-31', '201406')

,('9111113', 'H1111LAC', '006', '2014-01-01', '2999-12-31', '201401')

,('9111113','H1111LAC', '006', '2014-01-01', '2999-12-31', '201402')

,('9111113','H1111LAC', '006', '2014-01-01', '2999-12-31', '201403')

,('9111113','H1111LAC', '006', '2014-01-01', '2999-12-31', '201404')

,('9111113','H1111LAC', '006', '2014-01-01', '2999-12-31', '201405')

,('9111113','H1111LAC', '006', '2014-01-01', '2999-12-31', '201406')

,('9111114','H1111LAC', '006', '2014-01-01', '2014-02-28', '201402')

,('9111114','H1111LAC', '006', '2014-04-01', '2999-12-31', '201404');

-- THIS IS WHAT YOU NEED:

WITH cte_History (CUSTOMER, PLANNBR, SUBPLAN, STARTDATE, ENDDATE)

AS

(

SELECT 9111111, 'H1111LAC','006', '2014-01-01', '2014-05-31' UNION ALL

SELECT 9111111, 'H1111OC','010', '2014-06-01', '2999-12-31' UNION ALL

SELECT 9111112, 'H1111LAC','006', '2014-01-01', '2014-05-31' UNION ALL

SELECT 9111112, 'H1111LAC','018', '2014-06-01', '2999-12-31' UNION ALL

SELECT 9111113, 'H1111LAC','006', '2014-01-01', '2999-12-31' UNION ALL

SELECT 9111114, 'H1111LAC','006', '2014-01-01', '2014-02-28' UNION ALL

SELECT 9111114, 'H1111LAC','006', '2014-04-01', '2999-12-31'

)

SELECT * FROM cte_history;

-- My not-so-optimal solution

WITH base AS

(

SELECTCUSTOMER,

PLANNBR,

SUBPLAN,

STARTDATE

FROM HISTORY

GROUP BY CUSTOMER, PLANNBR, SUBPLAN, STARTDATE

)

SELECT DISTINCT b.*, MAX(ENDDATE) OVER (PARTITION BY b.CUSTOMER, b.PLANNBR, b.SUBPLAN, b.STARTDATE)

FROM base b

CROSS APPLY HISTORY h

WHERE h.CUSTOMER = b.CUSTOMER

AND h.PLANNBR = b.PLANNBR

AND h.SUBPLAN = b.SUBPLAN

AND h.STARTDATE = b.STARTDATE;

Edit: code formatting.