This page of the Spider-Man Miles Morales game guide contains information about the costume called the Bodega Cat Suit.
Costume received after completing the game's main storyline and side missions: Looters and Cat's Pajamas. It does not have any modifications.
Another combination of the Classic Costume, this time the outfit comes with a sweatshirt and a backpack with furry contents. A cat named Spider-Man with his own mask not only looks adorable, but he can also scratch enemies while performing finishing blows!