great job on giving us the setup DDL and Data.
Your data has all the same datetimes, so it'll probably look better when you compare the example with real data.
this seems to work for me, is this what you are after?
SELECT
ID,
PO,
CASE WHEN ISNULL(timestamp1,'1900-01-01') >= ISNULL(timestamp2,'1900-01-01')
AND ISNULL(timestamp1,'1900-01-01') >= ISNULL(timestamp3,'1900-01-01')
AND ISNULL(timestamp1,'1900-01-01') >= ISNULL(timestamp4,'1900-01-01')
THEN ISNULL(timestamp1,'1900-01-01')
WHEN ISNULL(timestamp2,'1900-01-01') >= ISNULL(timestamp1,'1900-01-01')
AND ISNULL(timestamp2,'1900-01-01') >= ISNULL(timestamp3,'1900-01-01')
AND ISNULL(timestamp2,'1900-01-01') >= ISNULL(timestamp4,'1900-01-01')
THEN ISNULL(timestamp2,'1900-01-01')
WHEN ISNULL(timestamp3,'1900-01-01') >= ISNULL(timestamp1,'1900-01-01')
AND ISNULL(timestamp3,'1900-01-01') >= ISNULL(timestamp2,'1900-01-01')
AND ISNULL(timestamp3,'1900-01-01') >= ISNULL(timestamp4,'1900-01-01')
THEN ISNULL(timestamp3,'1900-01-01')
WHEN ISNULL(timestamp4,'1900-01-01') >= ISNULL(timestamp1,'1900-01-01')
AND ISNULL(timestamp4,'1900-01-01') >= ISNULL(timestamp2,'1900-01-01')
AND ISNULL(timestamp4,'1900-01-01') >= ISNULL(timestamp3,'1900-01-01')
THEN ISNULL(timestamp4,'1900-01-01')
END As MaxDate
FROM [Dates]
Lowell