We present highly selective Rh-catalyzed reductive amination (RA) with integrated recycling of the homogeneous catalyst via a thermomorphic multiphase system (TMS) in a continuous-flow miniplant. Methanol, as a green alternative, was used as the polar solvent. In continuous operation for over 90 h and without catalyst makeup, the yield of the desired tertiary amine was constantly over 90%. For the first time in RA, additional continuous removal of the coproduct water was successfully implemented via an organic solvent nanofiltration (OSN) membrane, keeping the water concentration constant below 3.1 wt % and showing the highest catalyst rejection (>99.7%). Rhodium loss via the product phase was unprecedentedly small, with only 0.003% per hour, a value never achieved with any known TMS system so far. This value corresponds to a concentration of 33 ppb in the product phase and only 0.6 mg Rh loss per kg of produced amine. The present study gives a very optimistic outlook for the potential of TMS as a catalyst recycling method for continuous chemical processes, given its excellent performance in the most relevant areas, such as reaction yields and catalyst stability/retention, as well as the removal of coproducts.