Вам необходимо указать таблицу в операторе SET, так как поля неоднозначны.
UPDATE table1
INNER JOIN table2 ON table2.id = table1.pid
INNER JOIN table3 ON table3.id = table2.cid
----- (Option1 - Shifting values in a single table) -----
SET
table1.col1 = table1.col2,
table1.col2 = table1.col3,
table1.col3 = table1.col4
----- (Option2 - Assigning values across tables) -----
SET
table1.col1 = table2.col2,
table2.col1 = table3.col2,
table3.col1 = table1.col2
----- (Option2 - Updating values across tables) -----
SET
table1.col1 = table1.col2 + 1,
table2.col1 = table2.col2 - 1,
table3.col1 = table3.col2 + table3.col1
WHERE
table1.id = 5
NB: SET commands are done in the order listed so may you need to swop the two lines around in the set to get what you want.
SET
table1.col2 = table1.col1 + 5,
table1.col1 = "1+2+3"