For example, four Compile-developed games on the system were published by Naxat... But only two of them actually mention Compile on the title screen. The other two don't mention Compile anywhere at all, to the best of my knowledge.
As far as I know, Naxat published Spriggan and Spriggan II that I know for sure are Compile games. But what about the 2 others? Gunhed was published by Hudson and Sylphia by Tonkin House. There's no other Compile game published by Naxat I can think of.
Compile had two other games published by Tonkin House in addition to Sylphia:
Cyber Knight & Cyber Dodgeball. Cyber Knight was conceived and designed by Group SNE who took a RED-like role, while Compile did the actual programming, graphical art, and music. Cyber Dodgeball is all Compile, to the best of my knowledge.
The two other Naxat published Compile games are Alien Crush and Devil's Crush. Alien was a Compile project from start to finish, but I guess RED handled concept design for Devil while Compile did the programming et al.