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Default Array Formula

I have an array formula that is summarising data from 3 spreadsheets,
however, I need to know how I can modify part of the formula so it will sum
different data. If you look at the formula you will see that it is
summarising the data where there is nothing in column F, however, I need to
be able to modify the formula so that it will sum both cells that contain
nothing and also if they contain certain phrases within a string of text.
There are possibly a dozen different variations and the cell can also contain
dates. I am not so bothered about the dates as these will all be different,
it is only if the cells that contain phrases that I am trying to identify and
summarise.

"=SUM((Sheet2!$C$3:$C$31="HEO")*(Sheet2!$F$3:$F$31 ="")*Sheet2!$G$3:$G$31)+SUM((Sheet3!$C$3:$C$68="HE O")*(Sheet3!$F$3:$F$68="")*Sheet3!$G$3:$G$68)+SUM( (Sheet4!$C$3:$C$53="HEO")*(Sheet4!$F$3:$F$53="")*S heet4!$G$3:$G$53)"

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