Through different methods, the Super Saiyan 2 state can be powered up from it's ordinary power boost into a much stronger state.
Aside from Super Saiyan Anger, the strengthened Super Saiyan 2 states are identical to the ordinary Super Saiyan 2 form, however when powering up into it the user possesses more sparks in their aura and their hair becomes even more spiked.
Usage and power
The first time a Super Saiyan 2 with power beyond the norm appears is in Dragon Ball Z: Battle of Gods, where Vegeta enhances his Super Saiyan 2 form with the Quake of Fury. This allowed Vegeta to power up his Super Saiyan 2 form to a level far above Super Saiyan 3.
In the Dragon Ball Super manga it is revealed that like how the original Super Saiyan form could be upgraded through training to gain power enhancements or become mastered, the Super Saiyan 2 form can be improved as well. By training yourself to deal with the Super Saiyan 2 form, you gain the ability to power up into this enhanced state. The weakest strengthened Super Saiyan 2 state displayed by Future Trunks is far more powerful than the Super Saiyan 2 state, as it increases the user's power as much as a Super Saiyan 3 (around four times greater than the regular Super Saiyan 2). Eventually, after training with Vegeta, Future Trunks became stronger in this state, able to hold his own against Goku Black as a Super Saiyan Rosé and Future Zamasu long enough for Goku and Vegeta to travel back to the present.
Against Super Saiyan Goku Black, Vegeta displayed his strengthened Super Saiyan 2 state, overwhelming Goku Black despite his base form alone being a match for Goku's Super Saiyan 3.
In the manga, Future Trunks managed to obtain this form through intense training after realizing that Super Saiyan 2 was not his limit. Future Trunks reveals this form to Goku during their sparring match when Goku transforms into a Super Saiyan 3 to impress Future Trunks - to which Future Trunks responds by taking on this state, prompting Vegeta to note with surprise that Future Trunks' strength was a match for Super Saiyan 3 Goku's, and requiring Goku to become a Super Saiyan God to take down Future Trunks. Future Trunks uses this form once again in the future, able to briefly take on Super Saiyan Rosé Goku Black and take down Future Zamasu. However, once Goku and Vegeta travel back to the present, Future Trunks is beaten down easily in this state by Black. Later, Future Trunks uses this state again when confronting Goku Black to save Gowasu - with Black responding by transforming into Super Saiyan Rosé, Future Trunks manages to hold his own just long enough for Goku and Vegeta to return - though at that point Black has Future Trunks at his mercy.
In the anime through the power of rage and his Super Saiyan Third Grade state, Future Trunks is able to power up his Super Saiyan 2 form into Super Saiyan Anger. This powered up Super Saiyan 2 possessed power comparable to Super Saiyan Blue.
In the Tournament of Power, as Goku began fighting Caulifla, the latter showed her great desire to master Super Saiyan 3, to which Goku insisted that she wasn't ready for. He began testing her with various tactics to sharpen her instincts and improve her battle method. As she continued to adapt and pressure Goku, the Universe 7 Saiyan showed her how to enter this strengthened state, which she quickly reciprocated. When cornered by Ultra Instinct "Omen" Goku, Super Saiyan 2 Kefla underwent a fight or flight response and awakened a new unpleasant power in her Super Saiyan 2 state - causing her hair to become a dark green and energy to pour from her body. This power up was referred to as a "final weapon" by Vados. However she was still beaten by Goku, with the only good coming from the sudden change was a scuff on Goku's arm and slightly grazing his hair though Roshi stated that had the one of the lasers landed, Goku would have died.