-- *** Test Data ***
-- Please supply in consumable format
CREATE TABLE #t
(
	ID int NOT NULL
	,Dept int NOT NULL
	,[Address] varchar(30) NOT NULL
	,GroupID int NOT NULL
	,NewGroupID int NULL
)
INSERT INTO #t (ID, Dept, [Address], GroupID)
VALUES (165683, 32, 'PO BOX 602', 2),(165925, 32, 'PO BOX 562', 2),(165696, 50, 'PO BOX 602', 4)
	,(164356, 103, 'PO BOX 175', 6),(164356, 103, 'PO BOX 175', 6),(164368, 203, 'PO BOX 72', 19)
	,(165856, 264, 'PO BOX 562', 27),(164374, 302, 'PO BOX 39', 32),(164375, 303, 'PO BOX 368', 33)
	,(164375, 303, 'PO BOX 368', 33),(164375, 303, 'PO BOX 368', 33),(164375, 303, 'PO BOX 368', 33)
	,(165934, 303, 'PO BOX 175', 33),(165934, 303, 'PO BOX 175', 33),(164382, 406, 'PO BOX 72', 47)
	,(164421, 905, 'PO BOX 39', 57),(165616, 4310, 'PO BOX 368', 87),(165616, 4310, 'PO BOX 368', 87)
	,(165616, 4310, 'PO BOX 368', 87),(165616, 4310, 'PO BOX 368', 87),(166077, 4913, 'ROUTE 3', 89)
	,(165768, 5434, 'PO BOX 368', 91),(164905, 5434, 'PO BOX 368', 91),(165768, 5434, 'PO BOX 368', 91)
	,(164905, 5434, 'PO BOX 368', 91),(165768, 5434, 'PO BOX 368', 91),(164905, 5434, 'PO BOX 368', 91)
	,(164934, 5803, 'PO BOX 368', 92),(164934, 5803, 'PO BOX 368', 92),(164934, 5803, 'PO BOX 368', 92)
	,(164934, 5803, 'PO BOX 368', 92),(166095, 8040, 'ROUTE 3', 109),(165294, 9311, 'PO BOX 175', 115)
	,(165294, 9311, 'PO BOX 175', 115);
-- *** End Test Data ***

WHILE 1=1
BEGIN;
	WITH AddrGrps
	AS
	(
		SELECT ID, Dept, [Address], GroupID, NewGroupID
			,MIN(COALESCE(NewGroupID, GroupID)) OVER (PARTITION BY [Address]) AS MinGroupID
		FROM #t
	)
	,DeptGrps
	AS
	(
		SELECT ID, Dept, [Address], GroupID, NewGroupID
			,MIN(MinGroupID) OVER (PARTITION BY Dept) AS MinGroupID
		FROM AddrGrps
	)
	UPDATE DeptGrps
	SET NewGroupID = MinGroupID
	WHERE NewGroupID IS NULL
		OR NewGroupID <> MinGroupID

	IF @@ROWCOUNT = 0
		BREAK;
END;

select * from #t;