What is the effect of doubling layers of ballistic vests?  Is it merely additive, or is having two surfaces to penetrate more resistant than a single layer of equal thickness.

It should be a bit better than additive due to the bullet expanding/fragmenting/tumbling/slowing on its journey through the outer vest.  

But I wouldn't bet on it.  Nor do I find the idea of wearing multiple ballistic vests an appealing one from a bulk/weight/heat point of view.

This depends on how the panels are constructed to begin with.  However, if anything, having two ballistic panels is probably slightly less effective than having a single panel that is twice as thick.

Keep in mind that Kevlar panels are made of several layers of fabric to begin with.  Frequently the layers are only tacked to each other to make the vest flexible and thus more comfortable to wear.  

Unfortunately if the layers separate, the vest is more easily penetrated.  This is well known and has been the subject of much heated argument between the NIJ and various body armor manufacturers (in reference to testing procedures).  

The ballistic effectiveness of the panel can be improved by cross-stitching the layers to each other.  However, this makes the vest stiff and less comfortable.
 
Thus it seems likely that the looseness between the two separate panels would make it slightly weaker than a single panel of twice the thickness.

Further, as e8ght suggests, wearing two separate vests is likely to be totally unbearable.

If adding a 2nd vest for added protection, I personally would drop the idea, for the reasons mentioned in the above replies. I'd go for the kevlar vest with ceramic inserts. Bulkier: yes, heavier: yes, sweater: yes but on the flipside you have added protection from hi-vel "projectiles".

just my 2cts

C-2-6