Bortezomib (BOZ) is a proteasome inhibitor chemotherapeutic agent utilized to treat multiple myeloma and recently offered to cure melanoma. Bortezomib-induced neuropathy is one of the dose-limiting side-effects, which can be treated with antioxidants (e.g. alpha-lipoic acid-ALA and Vitamin B1-vit B1). We hypothesized that these antioxidants may counteract the antitumor activity by disrupting the BOZ-induced pathways (e.g. proteasome inhibition or reactive oxygen species generation). The objectives were: (i) to verify the anti-proliferative effect of BOZ; (ii) to compare the influence of the antioxidants on the antitumor effect of BOZ in melanoma (A2058) and myeloma (U266) cells. At first, the reduction in the anti-proliferative effect of BOZ by ALA was proved in melanoma cells. Analysis of p53 phosphorylation and the cell cycle progression revealed that ALA failed to counteract these effects of BOZ. Nevertheless, a good correlation was found between the inhibition of the anti-proliferative effect, the anti-proteasome activity and the oxidative stress level after the co-treatment with 20 ng/mL BOZ + 100 μg/mL ALA. Downregulation of apoptotic proteins such as HO-1 and Claspin along with the inhibition of the cleavage of Caspase-3 indicated the proteomic background of the altered responsiveness of the melanoma cells exposed to BOZ + ALA. This phenomenon draws attention to the proper application of cancer supportive care to avoid possible interactions.