child router question

Question

let's say we have a monorepo, one server, two client apps (cat and dog).  we make one appRouter, like:
export const appRouter = t.router({
  cat: catRouter,
  dog: dogRouter
})
export type CatRouter  = typeof catRouter;
export type DogRouter = typeof dogRouter;

the cat app should only know about cat routes, dog app only about dog routes by importing the right type.

the server will listen for /cat.getCatFood and /dog.getBone. either i want to change the dot to a forward slash so i can simply tell cat app the baseurl is /cat OR tell client, hey, baseUrl is  but, you should prefix all calls with "cat."
are either possible?