Several years ago, we detected the formation of multicellular spheroids in experiments with human thyroid cancer cells cultured on the Random Positioning Machine (RPM), a ground-based model to simulate microgravity by continuously changing the orientation of samples. Since then, we have studied cellular mechanisms triggering the cells to leave a monolayer and aggregate to spheroids. Our work focused on spheroid-related changes in gene expression patterns, in protein concentrations, and in factors secreted to the culture supernatant during the period when growth is altered. We detected that factors inducing angiogenesis, the composition of integrins, the density of the cell monolayer exposed to microgravity, the enhanced production of caveolin-1, and the nuclear factor kappa B p65 could play a role during spheroid formation in thyroid cancer cells. In this study, we performed a deep proteome analysis on FTC-133 thyroid cancer cells cultured under conditions designed to encourage or discourage spheroid formation. The experiments revealed more than 5900 proteins. Their evaluation confirmed and explained the observations mentioned above. In addition, we learned that FTC-133 cells growing in monolayers or in spheroids after RPM-exposure incorporate vinculin, paxillin, focal adhesion kinase 1, and adenine diphosphate (ADP)-ribosylation factor 6 in different ways into the focal adhesion complex.