The GreenBox+ technology is suitable to extract hemicellulose sugars prior to pulping of biomass into pulp products. The revenue obtainable from the sugar stream can significantly improve the economics of a pulp and paper mill. An initial extraction and recovery of sugars is followed by production of a pulp product with similar or better properties. Other co-products such as acetates and furfural are also possible. Some variations provide a process for co-producing pulp and hemicellulosic sugars from biomass, comprising: digesting the biomass in the presence of steam and/or hot water to extract hemicellulose into a liquid phase; washing the extracted solids, thereby generating a liquid wash filtrate and washed solids; separating the liquid wash filtrate from the washed solids; refining the washed solids at a refining pH of about 4 or higher, thereby generating pulp; and hydrolyzing the hemicellulose to generate hemicellulosic fermentable sugars.