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UPDATE TABLE_A a JOIN TABLE_B b ON a.join_col = b.join_col AND a.column_a = b.column_b SET a.c
Yes, you can do a 3 table join for an update statement. Here is an example :
UPDATE customer_table c JOIN employee_table e ON c.city_id = e.city_id JOIN anyother_ table a ON a.someID = e.someID SET c.active = "Yes" WHERE c.city = "New york";