The Box–Behnken design is a chemometric tool often used for the optimization of analytical methods. This tool enables quadratic models showing the critical condition (maximum, minimum or saddle point) to be obtained. The optimization of analytical methods involving two or more chemometric responses requires use of multiple responses. These multiple responses are established by considering the objective of the analytical system that is being optimized. The most common method employed to obtain multiple responses makes use of a desirability function, where individual response surfaces are determined for each response. An on-line sequential preconcentration system using chemically modified silica was developed for determination of Cr(III) and Cr(VI) by flame atomic absorption spectrometry. The optimization was performed using a multivariate methodology and a desirability function was established.