Operation: Inner Space

Operation: Inner Space is an action game developed in 1992 and published in 1994 by Software Dynamics for Windows. The player's mission is to enter the computer (represented by "Inner Space") in a spaceship and recover the icons and resources that have been set loose by an invasion, and ultimately to destroy the "Inner Demon". The player interacts with other spacecraft along the way, and can compete in races for icons.

You can choose a ship from one of six teams (there is also a seventh AI-only team), and interactions will depend almost entirely on which team you pick. All of the teams have relations with each other.