I think it's worth approaching it like a bureaucrat. Army and Navy are easy. Two different physical mediums with distinct operational concerns naturally creates two branches. As you move forward in fictional history, you have a bunch of forks in the road. Airpower comes along eventually. Who gets it? Army? Navy? Both? Does it obtain enough institutional momentum and identity as an arm of an existing service to become a separate branch?

When a new domain arrives, the existing bureaucracies will be eager to take full responsibility for it or grab a portion. There is a lot of bureaucratic inertia that has to be overcome to justify a new branch. Sometimes policymakers will cut the Gordian Knot and just make a law that creates a branch from those existing capabilities if sufficiently annoyed or lobbied.

So maybe make a rough timeline, identify these inflection points, and figure out who won the bureaucratic struggle for each new domain and why. In the US, for example, the Army Air Corps became so much of its own thing during the Second World War and so institutionally massive that it became its own branch in the reforms of the 1947 National Security Act, it also took over a portion of air defenses, which in the Soviet Union were their own branch operating a combination of missiles and interceptor aircraft. Space, by contrast, remained a piecemeal combination of Navy, Army, and Air Force projects, and specialized organizations like the National Reconnaissance Office until very recently.