||The transition energy from galactic to extragalactic cosmic ray sources is still uncertain, but it should be associated either with the region of the spectrum known as the second knee or with the ankle. The baseline design of the Pierre Auger Observatory was optimized for the highest energies. The surface array is fully efficient above 3 x 10(18) eV and, even if the hybrid mode can extend this range below 10(18) eV, the second knee and a considerable portion of the wide ankle structure are left outside its operating range. Therefore, in order to encompass these spectral features and gain further insight into the cosmic ray composition variation along the transition region, enhancements to the surface and fluorescence components of the baseline design are being implemented that will lower the full efficiency regime of the Observatory down to similar to 10(17) eV. The surface enhancements consist of a graded infilled area of standard Auger water Cherenkov detectors deployed in two triangular grids of 433 m and 750 m of spacing. Each surface station inside this area will have an associated muon counter detector. The fluorescence enhancement, on the other hand, consists of three additional fluorescence telescopes with higher elevation angle (30 degrees-58 degrees) than the ones in operation at present. The aim of this paper is threefold. We study the effect of the segmentation of the muon counters and find an analytical expression to correct for the under counting due to muon pile-up. We also present a detailed method to reconstruct the muon lateral distribution function for the 750 m spacing array. Finally, we study the mass discrimination potential of a new parameter, the number of muons at 600 m from the shower axis, obtained by fitting the muon data with the above mentioned reconstruction method. (C) 2008 Elsevier B.V. All rights reserved.