Simulated moving bed (SMB) chromatography is an important technique for the continuous separation of valuable products. Recently suggested process modifications have shown the potential for further improvement. In this work, a concept is presented that combines non-permanent product withdrawal at one or both outlet ports (leading periodically to a "product" and a "non-product" fraction) with an internal recycle and re-feeding of the "non-product" fraction in alternation to the original feed mixture. Using simulation studies for linear and non-linear isotherms, it was shown that in terms of process performance and product recovery, this fractionation and feed-back approach (FF-SMB) is superior to both the conventional SMB process as well as to a previously reported fractionation and discard strategy.