Huh! I think this is the first isekai I've read where the reincarnate co-exists with her host. It's usually a sorta 'overwrite' thing.
I know of two others at least.
Isekai Soudouki has a samurai and a modern otaku act as the cheerleading squad for the main character, who is the native soul of the body and is in control (aside from the samurai occasionally taking over for stronger enemies).
There is also Two As One Princess, in which the protagonist is possessing a girl and they basically travel around the world doing isekai stuff. It's marked as gender bender and shoujo ai, but given that there is only one body and one of the two is a sexless ghost (uses female mannerisms early on to reassure the little girl he possesses, not sure about after that cuz I stopped reading after a while).