Renee, I am very sorry that my answer is not going to be a happy one, but it is honest and it is said with great concern. You have a 4 mo old pit bull mix. Do not add another dog. PB are bred to be dog aggressive. They almost ALWAYS do great with other dogs until they mature. I cannot begin to count even in just one year the number of people who post on the aol boards about their maturing PB or PBmix killing their other pets. They are always SOOOOO shocked as they just LOVED EACH OTHER… til that day.
Many PB and PB mixes do great with other dogs and pets. But you don't know til they mature if they will. It is the one reason I support shelters euthanizing them all (and Rotties and chows) except when a breed rescue takes them. There are dogs (and btw I have chows and rotties) who simply need homes that are experienced with that breed to own, and PB are one of them. People with PB experience get them KNOWING that when the dog matures, they may have to safely keep them away from every other pet... and they are physically, emotionally, and financially able to provide that type of separation. IF you are, then you might consider another pet now. But get the pet for YOU, not for the sad PBmix.
And frankly, because Basenji can also be snots about other dogs, I would consider a much much more "pack" oriented dog breed that is KNOWN to not be dog aggressive if you want a new pet.
And please, let Basenji rescue know about this fellow so they can help with him.