MySQL 8.0

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CREATE TABLE table1
    (`User` varchar(10), `Market` varchar(3), `Purchase_ID` int)
;
    
INSERT INTO table1
    (`User`, `Market`, `Purchase_ID`)
VALUES
    ('John Smith', 'NYC', 1),
    ('John Smith', 'NYC', 2),
    ('Bob Miller', 'NYC', 2),
    ('Bob Miller', 'NYC', 4),
    ('Tim Wilson', 'NYC', 3)
;
SELECT 
  user,
  COUNT(DISTINCT purchase_id)
  ,MAX((SELECT COUNT(DISTINCT purchase_id) FROM table1 WHERE `Market` = t1.`Market` )) bymarkte
FROM table1 t1
GROUP BY 1


user
COUNT(DISTINCT purchase_id)
bymarkte


Bob Miller
2
4

John Smith
2
4

Tim Wilson
1
4


SELECT 
  user,
  COUNT(DISTINCT purchase_id)
  ,MAX(countr) bymarkte
FROM table1 t1
INNER JOIN (SELECT `Market`,COUNT(DISTINCT purchase_id) countr FROM table1 GROUP BY  `Market` ) ta ON t1.`Market` = ta.`Market`

GROUP BY 1


user
COUNT(DISTINCT purchase_id)
bymarkte


Bob Miller
2
4

John Smith
2
4

Tim Wilson
1
4