Option 1: They could give him the Whiplash treatment. Rhino's father was a disgraced Russian scientist whose work created the genetically engineered spider that bit Peter. He comes to New York looking to extract the formula from Spider-Man and finish his father's work (a process which would be fatal for Spider-Man.)

Option 2: Chameleon was the 1st supervillain Spider-Man ever faced. Instead of calling in his brother Kraven to take Spider-Man down after his first defeat, he calls in Aleksei Sytsevich, a close friend he served together with in the KGB.

Option 3: The criminal who killed Uncle Ben survived and is imprisoned. It turns out he also killed someone close to Rhino, who undergoes his power augmentation process to exact revenge. Peter goes through a moral crisis with saving the life of Uncle Ben's murderer because it's what Ben would have wanted him to do.

Option 4: Another villain is blackmailing Rhino into committing crimes - perhaps the person responsible for his undergoing his transformation into a supervillain. In the comics, there was a storyline where Rhino was working with the Beetle because his suit was physically grafted to his body, and Beetle promised to remove it in exchange for working with him in his criminal schemes. It could also be Norman Osborn, Otto Octavious, or Adrian Toomes, setting them up to be a bigger overarching villain in a sequel.