A process and apparatus for catalytic reforming of hydrocarbons wherein the effluent stream from the first and/or second reactor of a reforming train with several reactors in series is cooled in a multistage process to remove aromatic compounds in the reacting medium prior to being reheated and returned to subsequent reactors for additional reaction to occur. The partial removal of aromatic compounds enhances the driving force for the conversion of paraffins and naphthenes by making the equilibrium more favorable to such conversion. The removal of aromatic compounds reduces the size of downstream process equipment thereby reducing capital costs and lowering energy usage. It is possible to add additional feed streams to reactors downstream of the intermediate reactor effluent cooling step thereby making the process unit capable of processing more feedstock to produce more product.