This should actually be done with multiple filter calls like:
$DeleteQuery->addFilter("psaType", "=", "i", "".$companyType ."");
$DeleteQuery->addFilter("psaProject", "=", "i", "".$projectTarget ."");
You can add multiple filters manually, it just isn't supported from the interface. They are always joined with AND and you can add as many as you want.
I don't think your example would work. I believe the second filter is ignored.