The Generalized Local Discriminant Bases (GLDB) algorithm proposed by Kumar, Ghosh and Crawford in [Best-bases feature extraction algorithm for classification of hyperspectral data], is a effective feature extraction method for spectral data. It identifies groups of adjacent spectral wavelengths and for each group finds a Fisher projection maximizing the separability between classes. The authors defined GLDB as a two-class feature extractor and proposed a Bayesian Pairwise Classifier (BPC) building all pairwise extractors and classifiers followed by a classifier combining scheme. With a growing number of classes the BPC classifier quickly becomes computationally prohibitive solution. In this paper, we propose two alternative multi-class extensions of GLDB algorithm, and study their respective performances and execution complexities on two real-world datasets. We show how to preserve high classification performance while mitigating the computational requirements of the GLDB-based spectral classifiers.