Although it sounds like Fordham has a smaller class size than Columbia, I would bet that if Fordham allowed junior year transfer students while you were there, some of these people would not be widely known to the class.
Even then.
I was a senior year transfer student and people knew who I was from my alma mater.
Actually they would be well known within their major area because students know most folks in their major, and newcomers would stand out. Bill Clinton went to Georgetown. As I went to a Jesuit HS a good number of my classmates went to G’town.When Clinton ran for POTUS my classmates who had gone to Gtown and whom I kept in contact ALL knew Clinton, even though he was a year ahead of them. They KNEW him. No one, as far as I know claims to know Obama from Columbia.