If the plugins all work by using their own game instance class, then their are either somewhat old (as in made before subsystems were a thing) or badly made. A good plugin would use a game instance subsystem, this way you can have multiple plugins that work independently without running into this issue.
You can only have exactly one game instance class that is used by the application. And since you cannot utilize multiple inheritance, there is no way to easily merge the multiple child classes into one. You would either have to extract the functionality for each of the plugins into separate game instance subsystems or copy them all into your own game instance implementation.