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Precise prediction of adsorption in a multicomponent system is vital for successful design of dye-contaminated industrial wastewater treatment processes. The present work looks for the reason behind the failure of the competitive Langmuir model (CLM) to describe adsorption in such systems, while the Langmuir model (LM) successfully describes the process for a single dye solution. With that end, derivations of LM and CLM have been revisited, and a criterion for the universality of active sites has been defined. Attempts have been made to describe the competitive adsorption based on the LM parameters determined from single dye solutions. Three dyes (safranin, crystal violet, and methylene blue) and two adsorbents [activated carbon (AC) and coconut fiber (CF)] are subjected to adsorption and BET tests. AC complies with the universality criterion, while CF does not. The active site density estimated from dye adsorption is 14-18 folds lower for AC and 18-38 folds higher for CF, than those done from the BET test. The CLM predicts the equilibrium adsorption density of both adsorbents in binary dye systems satisfactorily, but there is a large gap between the predicted and experimental values of equilibrium concentration. It is argued that in liquid systems, adsorption occurs through different types of interactions, and hence the adsorption process even for a single dye should not be presented by a single K L value (as is formulated in LM), rather with multiple K L values corresponding to the interaction types. These K L values will classify the active sites as universal and specific in a multicomponent system, and then the CLM will predict competitive adsorption better, which will make the adsorption process design more precise.