Do we have enough information to determine Severus Snape's Meyers-Briggs type?

One of recent SFF.SE answers alleged that Snape is an INTJ, and there was a disagreement of whether we can really know that.

Do we have enough information to determine Severus Snape's Meyers-Briggs type? If so, what is it likely to be?

P.S. I'm aware that not everyone neatly fits into a single M-B type, myself included, so an answer that legitimately says "part X and part Y" is quite acceptable.

The reasoning must be fully based on canon info (books/Pottermore/WoG) and standard M-B guidelines.