A three-cell, continuous-flow electrochemical reactor is numerically simulated, revealing multiple steady states in terms of production rate. The bipolar electrochemical reactor fluorinates organic compounds in liquid solution in parallel flow cells, accompanied by the generation of hydrogen gas. The mathematical model of two-phase flow, phase equilibrium, gas-phase molecular association, and thermal energy considerations by Drake et al. (Ind. Eng. Chem. Res. 2001, 40, 3109; J. Electrochem. Soc. 1998, 145, 1578) is extended to address interactive multiple cells. Necessary model extensions include intercell heat transfer through the bipolar electrodes, inlet flow-distributor connectivity, and serial current redistribution. Multiphase heat transfer, among these other cell-to-cell interactions, affects the occurrence of multiple states and profiles within differently operating parallel cells. A trifurcation point occurs at 17.3 V in the operating curve of total current versus applied potential. Here, this three-cell production rate curve branches into three possible steady states of one, two, or three high-potential, inefficient cells. These states are unfavorable in terms of power consumption because the same total current can be accomplished by an efficient state requiring less potential. The pressure profiles of an inefficient state also reveal that the system is vulnerable to physical failure with the collapse of the narrow flow channels.