Capacitor with n electrodes
Assuming the plates are connected in an interleaved fashion as normal, there are n-1 gaps with n electrodes. Each one acts as a capacitor in parallel with the others.

Here is an image from this website. 

 

You can see that there are 11 plates and 10 gaps resulting in effectively 10 parallel capacitors of area equal (approximately) to the area of the dielectric slabs.