Hemodialysis (HD) has limited efficacy towards treatment of drug toxicity due to strong drug-protein binding. In this work, we propose to infuse a competitor drug into the extracorporeal circuit that increases the free fraction of a toxic drug and thereby increases its dialytic removal. We used a mechanistic model to assess the removal of phenytoin and carbamazepine during HD with or without binding-competition. We simulated dialytic removal of (1) phenytoin, initial concentration 70 mg/L, using 2000 mg aspirin, (2) carbamazepine, initial concentration 35 mg/L, using 800 mg ibuprofen, in a 70 kg patient. The competitor drug was infused at constant rate. For phenytoin (~ 13% free at t = 0), HD brings the patient to therapeutic concentration in 460 min while aspirin infusion reduces that time to 330 min. For carbamazepine (~ 27% free at t = 0), the ibuprofen infusion reduces the HD time to reach therapeutic concentration from 265 to 220 min. Competitor drugs with longer half-life further reduce the HD time. Binding-competition during HD is a potential treatment for drug toxicities for which current recommendations exclude HD due to strong drug-protein binding. We show clinically meaningful reductions in the treatment time necessary to achieve non-toxic concentrations in patients poisoned with these two prescription drugs.