The work of Benjamin, Mullin, Pfister and others on the non-uniqueness of solutions of the Navier–Stokes equation in Couette flow at small aspect ratio has revealed the existence of ‘anomalous’ 1-cell modes. A natural question to ask is whether these ‘anomalous’ modes are robust enough to survive the application of a body force, such as an externally applied magnetic field. We find that the answer is positive, although, with increasing magnetic field, steady 2-cell flows are generally more stable than 1-cell states. We also show that new time-dependent flows are easy to excite at relatively low Reynolds numbers compared to the case without a magnetic field, and we present two such flows.