What if the Romans decided that imminuty from prosecution during someone's term of office was not sicha good idea, and removed their protections?
Follow up: How on Earth could you convince the (office holding) Romans this would be a good idea? Perhaps a Plebeian uprising led by some zealous tribunes? Or perhaps something more convoluted, such as the realization that the immunity encouraged the advancement of corrupt officials, and that the ending of that immunity would encourage officials (corrupt or otherwise) to pursue rash actions (Caesar crossing the Rubicon comes to mind).