At this point there is still a main storyline, but you are free to ignore it completely if you want. You can develop your space empire in any direction you desire. You can be a warmonger, a peacemaker, a diplomat, a merchant, or any combination of those. You can destroy planets, betray allies, terraform planets, raise up lower life forms to sentience, and a whole host of other things. This is when the real sandbox nature of the game reveals itself and you might spend as much time imagining the things you want to do as you spend actually doing them.
The game allows this type of creativity by not putting any real restraints on what you want to do. You can go anywhere and do almost anything. You are definitely the super star of the universe, so if you put your mind to it you can accomplish anything for your space culture.
One of the best things about this stage is the fact that the majority of the time you will create your own goals for yourself. In any game, goals that you create for yourself are always more rewarding, exciting, and memorable than goals you achieve because the game says you should achieve them.
This is also where a lot of the "Sim-like" stories will develop among players. When a game lets you craft your own stories the opportunities for long term play are tremendous. With so much to do in this stage, the opportunities for developing hilarious or exciting stories about your race are limitless.