The Spider-Man Miles Morales cat suit lets you fight crime with a cat. Why wouldn't you want that? Spider-cat, complete with his own mask, even helps out with your finishing moves and leaps from the backpack for swipe or two at enemies as yoiu fight. However, don't expect to get this suit quickly though because you'll have to finish the game before you can put it on. You meet Spider-cat much earlier in the but you can't bring him along until after the story's complete. Which does suck a touch. However, here's what you need to do in order to (eventually) unlock the Spider-Man Miles Morales Spider-Cat suit.
1. Complete the mission Looters!!!
After you complete the train mission for Uncle Aaron and destroy all the bombs, you'll unlock a side mission called Looters!!! in Harlem. This mission will eventually introduce you to Spider-Cat, once you've rescued him that is. Head to the marker to find Teo's Grocery/Bodega, where Teo will tell you he was robbed and the thieves took Spider-Cat.
Obviously this won't stand, and as the friendly neighborhood Spider-Man you'll have to do something about it. Head to the new marker that appears once you've finished talking to Teo and play through the mission. You'll need to battle a few waves of thugs and get the power back on, after they tried to turn it off.
Once everyone's defeated and you've saved the day, you'll meet Spider-Cat in the fur.
2. Finish the game to finally unlock the Spider-Cat suit
When the credits have rolled and you're back in the world to mop up extras you'll get another side mission, called The Cat's Pajamas, marked at Teo's Store. Head over there and you'll be able to pick up Spider-Cat, which will unlock the Bodega Cat suit. Not only will your new friend pop out of the bag to take in the sights as you swing around, but he'll also throw a claw in whenever you perform a finisher. Good cat.