The only way to get Starveling Cats without the help of another player is through a Bundle of Oddities. It’s how I got mine (I didn’t even want it. I was just trying to get my soul back). Thing is that it only shows up at a value of 99 so its a game of luck if that’s the way you go.
See here: Bundle of Oddities (Guide) - Fallen London Wiki
2 Likes