This category by its name sounds like the opposite of "defective" where one or more usual forms are absent, generally used of verbs.
While I'm not sure whether this category of nouns exists in English I can think of a couple of English nouns that have more than one plural with differing senses (two plurals with the same sense is much more common).
The most commonly discussed example is probably fish.
- Plural 1 is the irregular plural actually taking the same form as the singular fish.
- Plural 2 is the regular plural fishes but is a bit more specialized.
Another one I came across through participation in Wiktionary is datum.
- Plural 1 is the irregular plural also alternatively (and sometimes controversially) used as a mass noun data.
- Plural 2 is the quite unexpected regular plural used only in specialized fields datums.
Which reminds me of another, also controversial case of multiple singular forms, but not so straightforward:
- Dice is the accepted plural of die but dice is also in common use as a singular in which case it is an invariant noun.
(links and stuff coming...)