We study the breakdown of a random fiber bundle model (RFBM) with n discontinuities in the threshold distribution using the global load sharing scheme. In other words, n+1 different classes of fibers identified on the basis of their threshold strengths are mixed such that the strengths of the fibers in the ith class are uniformly distributed between the values σ2i-2 and σ2i-1, where 1≤i≤n+1. Moreover, there is a gap in the threshold distribution between ith and (i+1) -th class. We show that although the critical stress depends on the parameter values of the system, the critical exponents are identical to that obtained in the recursive dynamics of a RFBM with a uniform distribution and global load sharing. The avalanche size distribution, on the other hand, shows a nonuniversal, non-power-law behavior for smaller values of avalanche sizes which becomes prominent only when a critical distribution is approached. We establish that the behavior of the avalanche size distribution for an arbitrary n is qualitatively similar to a RFBM with a single discontinuity in the threshold distribution (n=1), especially when the density and the range of threshold values of fibers belonging to strongest (n+1) -th class is kept identical in all the cases. © 2008 The American Physical Society.