Brewer’s spent grain (BSG) is an undervalorized organic feedstock residue composed of fermentable macromolecules, such as proteins, starch, and residual soluble carbohydrates. It also contains at least 50% (as dry weight) of lignocellulose. Methane-arrested anaerobic digestion is one of the promising microbial technologies to valorize such complex organic feedstock into value-added metabolic intermediates, such as ethanol, H2, and short-chain carboxylates (SCC). Under specific fermentation conditions, these intermediates can be microbially transformed into medium-chain carboxylates through a chain elongation pathway. Medium-chain carboxylates are of great interest as they can be used as bio-based pesticides, food additives, or components of drug formulations. They can also be easily upgraded by classical organic chemistry into bio-based fuels and chemicals. This study investigates the production potential of medium-chain carboxylates driven by a mixed microbial culture in the presence of BSG as an organic substrate. Because the conversion of complex organic feedstock to medium-chain carboxylates is limited by the electron donor content, we assessed the supplementation of H2 in the headspace to improve the chain elongation yield and increase the production of medium-chain carboxylates. The supply of CO2 as a carbon source was tested as well. The additions of H2 alone, CO2 alone, and both H2 and CO2 were compared. The exogenous supply of H2 alone allowed CO2 produced during acidogenesis to be consumed and nearly doubled the medium-chain carboxylate production yield. The exogenous supply of CO2 alone inhibited the whole fermentation. The supplementation of both H2 and CO2 allowed a second elongation phase when the organic feedstock was exhausted, which increased the medium-chain carboxylate production by 285% compared to the N2 reference condition. Carbon- and electron-equivalent balances, and the stoichiometric ratio of 3 observed for the consumed H2/CO2, suggest an H2- and CO2-driven second elongation phase, converting SCC to medium-chain carboxylates without an organic electron donor. The thermodynamic assessment confirmed the feasibility of such elongation.