The main story is around Tavi. You can finish it already. There are some side stories that you can explore beside Socket and the lab assistant. For now you can do quests with Rahi, available from the start. Jacki who you can find in the gym. Artica who will arrive a few days after the game start. Alex, who is in the same room as Socket. And the slave market that unlocks after you get a few slaves in you cell, maybe needs to train them a bit.
All plot lines will tell you that is the end of the story, if you get that message move to the next story or keep doing the repeatable events.