Sogobudo means "holistic" or integrated budo, a concept in which a person searches for both the spiritual and technical oneness that unites budo--the commonality between all martial arts; karate and aikido and kendo share a common spiritual base, which should shape and inform technique.
For Egami sensei, form always followed spirit or feeling. The Sogobudo practitioner would use one particular martial art (usually Karate) as an entry to the larger holistic martial art of Sogobudo, for as Egami sensei saw it, all techniques are related.
Because Egami Sensei was the president of Shotokai, there were limits on what he could do himself; so he selected a small group of his best students at Chuo university to set up a group --a research and development wing of Shotokai-- to explore the possibilities of Sogobudo. He organized a team of about thirty young martial arts masters in various arts --Aikido, Karate, Judo, Kendo, Bojitsu, mostly recent university graduates, and they practiced in an open and exploratory way for about three years. From this practice was born at first Sogobudo, which quickly became Shintaido. The person behind all this was a young Chuo university karate man named Hiroyuki Aoki. He held the fifth dan under Egami and was the chief instructor at Chuo karate club.
Given the political delicacy of the situation --as many people thought he had already changed karate too much-- Egami sensei could not simply suspend Shotokai practice and go off to become the founder of Shintaido, but neither could the Shintaido group call themselves Karate. Aoki sensei left the Shotokai, with Fugaku Ito, a virtual co- founder of Shintaido, and other members of the Sogobudo group to found Shintaido. Today the group is called International Shintaido Federation, which now has about five thousand members --mostly in Japan and France. Sogobudo was more or less forgotten, though a few people still practice its karate aspect.
This is what is meant by Karate Sogobudo.
If you should want to know more about Shintaido there are many sites on the Web, here are a few:
Shintaido Home Page in Japan
Shintaido in UK
Shintaido in USA
They are, though, no longer involved in Shotokai practice directly, though they share a lot with Shotokai. Shintaido is a bit different.