We present a new Monte Carlo method for solving the population balance with multiple growth processes. The method samples a constant number of particles regardless of whether the actual growth process results in increase or decrease of the particle concentration. By decoupling the size of the simulated sample from the concentration of the actual system we achieve constant accuracy throughout the simulation. We apply this method to coagulation with simultaneous binary break-up. We examine the results for three cases with analytical solutions and show that the constant-N method yields accurate results.