Natsume Sōseki is actually considered as the greatest novelist in modern Japanese history and one of his best known novels is “I Am a Cat”.
Both, Fukuzawa and Odasaku, seem to have a connection to him in Bungou Stray Dogs. Natsume was mentioned by Fukuzawa in the last episode of the first season while talking to Fitzgerald and as we know he is also the man who encouraged Oda to become a writer. In Addition, both characters who met Natsume in the past or know him are shown with the same cat on the shoulder in official art, coincidence? + Dazai calling the cat “sensei” for unknown reasons.
(Let us not ignore the resemblance between the cat on the cover of the book and the cat in Bsd)
I’ll leave the rest up to your imagination~