The growth of high-quality in vitro potato plants (Solanum stenotomum subsp. stenotomum, Solanum stenotomum subsp. goniocalyx, and Solanum tuberosum subsp. andigena) is affected by multiple biological, operational, and environmental factors. Research on in vitro culture is frequently focused on the species, explant, composition of the culture medium, and incubation conditions, but only limited information is available on the effect of the gas exchange rate and volume of in vitro culture vessels under variable planting densities. In the present study, these factors were evaluated with a set of seven diverse potato landraces. The results were compared to the plants’ responses in routinely used in vitro culture vessels, i.e., 13 × 100 mm and 25 × 150 mm test tubes, and GA7® magenta vessels. In vitro potato plants grown in plastic vessels equipped with a HEPA filter delivering a high gas exchange rate developed thicker stems (0.95 mm), a higher total average leaf area (2.51 cm2), increased chlorophyll content in leaves (32.2 ppm), and lower moisture content in their tissues (90.1%) compared to filter systems with lower gas exchange rates. A high planting density of 10 × 10 plants per vessel (360 and 870 mL) negatively affected the average stem width and root length but increased the plant height (3.4 cm). High fluctuations of ion-uptake of NO3−, Ca++, K+, and Na+ were observed between genotypes, with some accessions having a 4.6-times higher Ca++-ion concentration in their tissues (190–234 ppm). The in vitro plants developed more robust stems, longer roots, and larger leaves within in vitro culture vessels equipped with a HEPA filter (high gas exchange rate) compared to the control vessels, in contrast to the chlorophyll content in leaves, which was higher in plants grown in narrow test tubes. Depending on the purpose of the subculture of in vitro plants, their growth and development can be molded using different gas exchange rates, planting densities, and vessel volumes.