You can of course use ‘OR’ to add additional logic to the whose filter with something like:
exists files "C:\setname.bat" whose (exists lines whose (it as lowercase contains "computer1\COMMON" as lowercase OR it as lowercase contains "computer2\COMMON" as lowercase OR it as lowercase contains "computer3\COMMONM" as lowercase) of it)
But if I’m understanding the scenario correctly, you might also simply be able to reference the computer name as well with something like:
exists files "C:\setname.bat" whose (exists lines whose (it as string as lowercase contains ((computer name & "\COMMON") as lowercase)) of it)