You might consider 'Tiger & Bunny'. It has heroes in a modern setting, similar to how Superman operates in a contemporary world. The characters have their own challenges and growth, similar to the journey of Superman.
I'd suggest 'One-Punch Man'. Both have characters with extraordinary powers and a sense of justice. However, the tone and style might be a bit different. Superman is more traditional heroic, while One-Punch Man has a comedic twist.
Well, 'Ultraman' could be one. It features powerful heroes defending against threats and has action-packed scenes similar to Power Rangers. Also, the concept of having a team of heroes working together is common in both.
I think there are a few. For example, some historical or mythological manga might share similar elements. But it really depends on your specific expectations.
I think 'Ouran High School Host Club' could be similar. It has a light-hearted and comedic tone with diverse and charming characters like in 'Fruits Basket'.
You might like 'Jujutsu Kaisen'. It has a similar theme of students learning and mastering their powers, along with a diverse range of personalities among the characters, much like in MHA.
Personally, I'd suggest Hunter x Hunter. It shares the elements of fantasy, adventure, and character development that are common in Fairy Tail and One Piece. The depth of the world-building and the complexity of the characters make it comparable.
I'd suggest 'Clannad'. It shares elements of heartfelt storytelling and explores various emotions, similar to what you find in 'The Promise'. There are touching moments and character arcs that might strike a chord if you enjoyed 'The Promise'.
Well, 'The Vampire Diaries' manga could be comparable. It shares the theme of vampire love and drama that Twilight is known for. Also, the character dynamics and emotional conflicts have some similarities.
I think 'Blue Period' could be similar. It also focuses on personal growth and relationships with a touch of emotional depth.
You could check out 'Sword Art Online'. Both it and 'Gamer' have elements of gaming, adventure, and character growth in a virtual setting. However, they also have their own unique twists and differences.
One manga that comes to mind is 'Neon Genesis Evangelion: The Shinji Ikari Raising Project'. It shares some similarities in themes and style with the original Evangelion.