I asked a question and got this reply which helped.
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
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]