The aim of this work was to prepare starch-based films plasticized with two and three-component deep eutectic solvents (DES) in the presence of different additives:aluminosilicates (sodium and calcium montmorillonite), microcrystalline cellulose, and tannin; and to investigate their influence on mechanical and barrier properties of the films. Mutual interactions between polysaccharide matrix, plasticizer, and additive were investigated by Fourier transform infrared (FTIR) spectroscopy. Two types of starches were used:native potato starch (TPS) and hydroxypropylated, oxidized potato starch (HOPS). The two-component DES CC:G consisted of choline chloride (CC) and glycerol (G), whereas the three-component DES with crosslinking activity CCit:U:G, included choline citrate (CCit), urea (U), and glycerol. For the TPS/CCit:U:G films an improvement of the mechanical and barrier properties was obtained after introduction of additives, whereas for TPS/CC:G only a slight decrease in water vapor transmission rate was observed, without any significant improvement in mechanical properties. Moreover, the mechanical test results, FTIR spectra, and the oxygen transmission rate values revealed that the clays interacted with plasticizer components, thereby hindering crosslinking reactions between plasticizer and starch.