A physicist in a collapsing Lagos discovers how to step sideways into parallel Earths and is immediately picked up by the Pandominion, an empire spanning a million versions of the world, run by the humans and animal-descended peoples who got there first. It’s at war with a machine civilization from another branch of the tree, and the war is going badly in ways nobody at the top will admit. Carey runs it through three characters, including a rabbit-descended soldier and a machine intelligence that becomes a person over the course of the book. Narrated from far in the future by something that says up front it was responsible for everything.
Infinity Gate