A system and process is disclosed for adding pre-fermentation separated non-fermentables, e.g., fiber, germ/oil, and/or protein, to a post-fermentation stream in a corn (or similar carbohydrate-containing grain) dry milling process for making alcohol and/or other biofuels/biochemical. The process includes mixing grain particles with a liquid to produce a slurry having starch and non-fermentables. The slurry is subjected to liquefaction to convert the starch in the slurry to complex sugars and produce a liquefied stream including the complex sugars and non-fermentables. After liquefaction but prior to fermentation of simple sugars resulting from conversion of the complex sugars, the non-fermentables are separated out to define a non-fermentables portion and an aqueous solution including the complex and/or simple sugars. The simple sugars are fermented to provide a fermented stream. Then, the separated non-fermentables portion is reincorporated back into the process into a post-fermentation stream. In one example, the non-fermentables may be mainly fiber.