Usa CASE expresiones para determinar la fecha reciente, la segunda y la más antigua. Póngalos en un CTE y use los nombres de las columnas en WHERE cláusula
WITH CTE AS(
SELECT *,
RecentDate =
CASE
WHEN APPR_DATE_1 >= APPR_DATE_2 AND APPR_DATE_1 >= APPR_DATE_3 THEN APPR_DATE_1
WHEN APPR_DATE_2 >= APPR_DATE_3 AND APPR_DATE_2 >= APPR_DATE_1 THEN APPR_DATE_2
WHEN APPR_DATE_3 >= APPR_DATE_2 AND APPR_DATE_3 >= APPR_DATE_1 THEN APPR_DATE_3
END,
SecondDate =
CASE
WHEN APPR_DATE_1 BETWEEN APPR_DATE_2 AND APPR_DATE_3 OR APPR_DATE_1 BETWEEN APPR_DATE_3 AND APPR_DATE_2 THEN APPR_DATE_1
WHEN APPR_DATE_2 BETWEEN APPR_DATE_1 AND APPR_DATE_3 OR APPR_DATE_1 BETWEEN APPR_DATE_3 AND APPR_DATE_1 THEN APPR_DATE_2
WHEN APPR_DATE_3 BETWEEN APPR_DATE_1 AND APPR_DATE_2 OR APPR_DATE_1 BETWEEN APPR_DATE_2 AND APPR_DATE_1 THEN APPR_DATE_3
END,
OldestDate =
CASE
WHEN APPR_DATE_1 <= APPR_DATE_2 AND APPR_DATE_1 <= APPR_DATE_3 THEN APPR_DATE_1
WHEN APPR_DATE_2 <= APPR_DATE_3 AND APPR_DATE_2 <= APPR_DATE_1 THEN APPR_DATE_2
WHEN APPR_DATE_3 <= APPR_DATE_2 AND APPR_DATE_3 <= APPR_DATE_1 THEN APPR_DATE_3
END
FROM #ASSET
)
SELECT
APPR_DATE_1, APPR_DATE_2, APPR_DATE_3, ID, NAME, ADDRESS
FROM CTE
WHERE
DATEDIFF(DAY, SecondDate, RecentDate) > 365
OR DATEDIFF(DAY, OldestDate, SecondDate) > 365
