My Hero Academia's League of Villains have largely taken a backseat to the new threat for Season 4 as Overhaul and the Shie Hassaikai have openly challenged them. After their violent first meeting, Overhaul and Shigaraki formed a pact that fans had not seen play out until the latest episode of the series. As Overhaul was only seeking to absorb the League of Villains due to the influence from their name in the criminal underworld, it appears that he had ideas for three of the League's members, Toga, Twice and Kurogiri.
But Episode 73 of the series revealed that Shigaraki also had his own plans for the Shie Hassaikai, and that involves two of his members that are currently working alongside the yakuza group as the pro heroes continue making their way through the base -- Toga and Twice.
Episode 73 brings the League of Villains back into the fold as Shigaraki has Toga and Twice working under Overhaul during his plan. But Shigaraki is cooking up something on his own as well as Toga and Twice ask him why they have to help Overhaul after he killed Magne. But Shigaraki revealed that this is merely a necessary step in whatever he's planning.
As the episode sees Toga and Twice start up chaos with the attacking pro heroes, it's also revealed that they aren't exactly hiding their ulterior motives. They are quite clear with Mimic, who is watching them within the walls, that they are only biding their time until they can get their "reward" which Toga hints that this is what Shigaraki is aiming for.
So while Overhaul clearly wanted to just use the League of Villains for his own means, Shigaraki isn't foolish either. Toga and Twice might have abilities that appealed to Overhaul and his plans, but they are also some of the more chaotic members of the League. They're going to do what they want, when they want to, so Overhaul should've been aware from the get go that Toga and Twice weren't really going to help out in any significant way. But now it's just a matter of seeing what they are really doing at the Shie Hassaikai base.
My Hero Academia was created by Kohei Horikoshi and has been running in Shueisha's Weekly Shonen Jump since July 2014. The story follows Izuku Midoriya, who lives in a world where everyone has powers, even though he was born without them. Dreaming to become a superhero anyway, he's eventually scouted by the world's best hero All Might and enrolls in a school for professional heroes. The series has been licensed by Viz Media for an English language release since 2015. My Hero Academia also launched its second big movie, Heroes Rising, in Japan this month.