High-value wood veneer is used in the furniture and automobile interior industries for decorative purposes. Due to mechanical restrictions, veneer application on surfaces is limited to simple shapes. In the last century, many approaches were developed to improve the moulding behaviour of veneer. However, all of these processes face several difficulties. Currently, water is primarily used for veneer plasticization, with the disadvantages of shrinkage and cracks due to drying. Furthermore, products often fail during material climate testing due to set recovery. Thus, a veneer modification process was considered combining plasticization, moulding, and shape fixation of veneer with reduced set recovery. To accomplish this, veneers were impregnated with furfuryl alcohol/maleic anhydride solutions to improve plasticization and moulding properties. Subsequently, veneers were moulded, and the realized shapes were fixed by temperature-induced acid-catalyzed polymerization. Due to the polymer in the cell wall, set recovery of all modified samples was noticeably reduced compared to reference samples plasticized with water prior to moulding. The degree of set recovery reduction due to modification varied with the modification intensity. Samples with higher weight percentage gain (WPG = 126.4%) were more stable in the presence of moisture than samples with lower polymer yields (WPG = 107.4%).