How to do 3 table JOIN in UPDATE query?

the answer is yes you can

try it like that

UPDATE TABLE_A a 
    JOIN TABLE_B b ON a.join_col = b.join_col AND a.column_a = b.column_b 
    JOIN TABLE_C c ON [condition]
SET a.column_c = a.column_c + 1

EDIT:

For general Update join :

   UPDATE TABLEA a 
   JOIN TABLEB b ON a.join_colA = b.join_colB  
   SET a.columnToUpdate = [something]

Alternative way of achieving same result is not to use JOIN keyword at all.

UPDATE TABLE_A, TABLE_B
SET TABLE_A.column_c = TABLE_B.column_c + 1
WHERE TABLE_A.join_col = TABLE_B.join_col

Below is the Update query which includes JOIN & WHERE both. Same way we can use multiple join/where clause, Hope it will help you :-

UPDATE opportunities_cstm oc JOIN opportunities o ON oc.id_c = o.id
 SET oc.forecast_stage_c = 'APX'
 WHERE o.deleted = 0
   AND o.sales_stage IN('ABC','PQR','XYZ')