If I reformat my 3DS, can I link to another Nintendo Network ID, and collect another Celebi from Pokebank?

[theSLAYER]

Hello all!

If I reformat my 3DS, can I link to another Nintendo Network ID, and collect another Celebi from Pokebank?

(If I can, I will be able to contribute my save for Celebi extraction, in the "Pokemon Link holding area")

EDIT:

I solved this problem without reformating.

I simply deleted the entire NNID account in my settings page and re-created it.

Note that any purchases, friends, miiverse content tied to the account will be lost (I didn't do any of those, so no harm for me)

Edited February 25, 2014 by theSLAYER