This paper presents a methodology for assessing mineral abundances of mixtures having more than two constituents using absorption features in the 2.1-2.4 μm wavelength region. In the first step, the absorption behaviour of mineral mixtures is parameterised by exponential Gaussian optimisation. Next, mineral abundances are predicted by regression tree analysis using these parameters as inputs. The approach is demonstrated on a range of prepared samples with known abundances of kaolinite, dioctahedral mica, smectite, calcite and quartz and on a set of field samples from Morocco. The latter contained varying quantities of other minerals, some of which did not have diagnostic absorption features in the 2.1-2.4 μm region. Cross validation showed that the prepared samples of kaolinite, dioctahedral mica, smectite and calcite were predicted with a root mean square error (RMSE) less than 9 wt.%. For the field samples, the RMSE was less than 8 wt.% for calcite, dioctahedral mica and kaolinite abundances. Smectite could not be well predicted, which was attributed to spectral variation of the cations within the dioctahedral layered smectites. Substitution of part of the quartz by chlorite at the prediction phase hardly affected the accuracy of the predicted mineral content; this suggests that the method is robust in handling the omission of minerals during the training phase. The degree of expression of absorption components was different between the field sample and the laboratory mixtures. This demonstrates that the method should be calibrated and trained on local samples. Our method allows the simultaneous quantification of more than two minerals within a complex mixture and thereby enhances the perspectives of spectral analysis for mineral abundances.