Jack meets a dog he simply names, Dog. Dog lasted in the Picture Text Comics for awhile, even garnering more air time then Max. He never was shown in the panel comics, and disappeared after the end of the Picture/Text Comics.
Dog became a major character with Max, and early on often competed with Max to be the top dog. It was not until later did it become clear they became friends. Dog and Max soon helped each other out and became good friends. Jack adopted Dog in the book, Adoption Who?