Storage unicorns and their hyped-up horns

What is or are "proboscii"?

The singular noun is proboscis. The root of the word is Greek, but it seems to have attained its current form in Latin. Regular Latin nouns ending -is have a nominative plural ending -es, so the inflected plural would be probosces. As we're speaking and writing modern English, it might be safer to say "proboscises".

Contrary to widespread belief on the Interwebs, no Latin words are pluralised by adding "ii" to their root. This fallacy probably arises from plurals like radii, but the "i" in radius is part of the root, not the inflected ending, and it is invariant through all cases and numbers.