multiple criterias in SUMIF formula

hi all,

is there any way for a sumif formula to have multiple criterias? for my case, after the formula checks for a condition, it has to check for another condition before summing up the figures.

this is my current formula:

=SUMIF(A:I,E2,F:F)

E2 contains a certain id and the formula will total up the figures in column F for that particular id. i want to add another condition that the formula has to check for another condition before summing up. it has to check the description in column C for these words 'OR'. only after that it can total up for the id AND with the words 'OR'.

i want to be able to use wildcards for 'OR' since the descriptions might contain 'AW OR', 'OR (ST)' etc.

how do i add the other condition into the formula? pls help.