One way to sense the presence of analytes in a solution is by exploiting surface plasmon resonance (SPR) at a metal/dielectric interface in the Turbadar–Kretchsmann–Raether (TKR) configuration. One of the ultimate goals of sensing is to be able to detect multiple analytes in a single solution simultaneously. Numerical studies show that two-analyte sensing can be achieved by having an artificial neural network (ANN) analyze reflectance data when either a columnar thin film (CTF) or a chiral sculptured thin film (CSTF) is used as the partnering dielectric material in the TKR configuration. Both CSTFs and CTFs are porous with the former being periodically non-homogeneous in the thickness direction. In addition, vertical multiplexing is to be incorporated in these sensors, as the two analytes were assumed in the theoretical model to be differentially concentrated around two different metal layers within each sensor. With respect to classifying nine different solutions, the CTF-based sensor with vertical multiplexing delivered a theoretical average accuracy of 92.3% while the analogous CSTF-based sensor delivered an average accuracy of 94.5%, with adequate training of the ANN. The non-SPR features in the reflectance data play a significant role in enhancing the accuracy of classification.