The aim of the current study was to systematically evaluate effects of single thiols, of thiol interactions in a single red wine matrix, and of red wine matrix effects combined with thiol interactions using projective mapping (PM) with experienced assessors. All work was done in dearomatized red wine from various cultivars. A dual approach to the projective mapping data analysis (coordinates and multifactorial analysis or frequency of citations and correspondence analysis), coupled to regression vector (RV) coefficients allowed to test the hypothesis that the resulting maps should be similar, which was the case for single thiols (RV > 0.7) but not for the more complex thiol × thiol or thiol × thiol × matrix interactions tested (RV < 0.7). It was shown that 4-mercapto-4-methylpentan-2-one (4MMP) levels were relatively more important than the cultivar used, while the opposite was true for 3-mercapto-1-hexanol (3MH) and 3-mercaptohexyl acetate (3MHA). No specific descriptors were associated with 3MH and 3MHA, but the wines had more “savory” notes. The interaction effects of 3MH × 4MMP and 3MHA × 4MMP were different both in the number and in the frequency of citation of the attributes. Practical Applications: Complex multilevel sensory interaction phenomena can be studied if a pragmatic and systematic practical methodology is used, as demonstrated by this work. As the method used does not require a trained panel, this type of approach can be used also outside an academic environment, to the benefit of the industry; however, the researchers must take into account the complexity of the matrix and the difficulty of the assessment. The outcome of the dual approach to the data analysis could help researchers decide which data handling option is better suited for their work.