The increasingly produced soybean molasses lacks value-added applications because its oligosaccharides stachyose and raffinose are poorly digestible/hydrolysable by many organisms. Enzymatic upgrading can be effective, but no study has previously examined and modeled its full complexity. This study addresses this knowledge gap by developing comprehensive models and evaluating them with results of enzymatic hydrolysis of, progressively, pure sucrose, melibiose, raffinose and stachyose, and then soybean molasses. The models considered all possible reaction pathways, competitive inhibition among substrates and intermediates, and kinetic decline of enzyme activities. The kinetic parameters, obtained from regression of concentration profiles for all carbohydrates (substrate, intermediates, and products), offered important insights into enzymatic hydrolysis of soybean galacto-oligosaccharides. Most importantly, digalactose was, for the first time, shown to form appreciably during stachyose hydrolysis (by breakage of mid-structure α-1,6 galactose-glucose bond), with rates comparable to the commonly recognized raffinose formation (by cleavage of terminal galactose). On the other hand, the invertase-catalyzed breakdown of stachyose to manninotriose (+ fructose) was much less significant. Further, the A. niger invertase could remove fructose from sucrose, raffinose, and stachyose, but with substantially different effectiveness: sucrose > raffinose > stachyose. Practically, the models developed are valuable to the development of enzymatic soybean-molasses upgrading process. • Upgraded soy molasses carbohydrate to sugars by A. niger enzyme. • Considered all reaction pathways, competitive inhibition, and enzyme deactivation. • Modeled hydrolysis of pure sucrose, melibiose, raffinose, stachyose, and molasses. • Digalactose found, for the first time, to form significantly from stachyose. • Invertase cleaved fructose (in descending rates) off sucrose, raffinose & stachyose.