Nope. PIR or other strictly motion based items are going to false at some point, period. There's a reason why they're typically only used to supplement cameras (or trigger a PTZ preset) or to assist security personnel in responding and evaluating a situation. The issue with either cross zoning or paralleling detectors is now you created the requirement for a long duration fault to generate an alarm (negating protection) or in the case of a cross zone pair or pool, you will constantly generate the trouble before the double knock occurs.
Example:
http://www.protechusa.com/Products/documents/XL2Med1.pdf
We have a zoo that has these set up and cross zoned and looking at only "controlled" spaces. They false. These are literally top of the line PIR based units. Same thing goes for the Redwalls and their contemporaries.
Next we move into something like scanning laser units, say a RLS-3060 or similar, they have a very narrow pattern and are designed as a single ended replacement for the old PE beams and similar.
http://www.optexamerica.com/sites/default/files/resource-uploads/RLS-3060SH.pdf
Put it this way, for one of those units, you're exceeding the cost that most have invested in their
entire system. A single PIR unit is a huge dent in the budget and still not false alarm proof.
Not to sound crass, but dealing with these systems, security and alarms, your common alarm or HA/security panel does NOT have the intelligence to discriminate and effectively process the alarms to be useful. Even large dollar access control systems don't have the HP without a lot of programming and thought.