To pluralize a word in Spanish you either add an '-s' or an '-es', an 'es' being necessary when the noun ends in a consonant. In Costa Rica I have heard the double plural for 'papases', with an '-s-es' ending.
In this context there is a possible reasonable explanation: If the regular plural form 'papás' refers to one set of parents, 'papases' could conceivably refer to a group of parents.
Regardless of the merits of this armchair etymology, the double plural appears to extend to other nouns whose last syllable is the tonic syllable. For example, I have heard 'mamases' and 'bebeses' (coming from 'bebé'), which contain the double plural, but cannot be rationalized as a group of plural elements.
Double plurals have arisen in other languages, but they usually occur when the former plural suffix becomes improductive. In Spanish, the '-s' and '-es' suffixes are entirely valid standing alone to pluralize their respective nouns, so I don't recommend using the double plural form. But it's sure fun to listen to :)
