Multilayer graded-bandgap avalanche photodiodes (APDs) are the future deterministic photomultipliers, owing to their deterministic amplification with twofold stepwise gain via impact ionization when operated in the staircase regime. Yet, the stepwise impact ionization irregularities worsen as the number of steps increases. These irregularities in impact ionization are the major source of noise in these APDs. These solid-state devices could replace conventional silicon photomultiplier tubes if they are carefully studied and designed. A noise model for multistep staircase APDs, considering equal stepwise ionization probabilities is previously reported. However, we derive a generalized noise model for multilayer graded-bandgap APDs, applicable for all operating biases, which include the sub-threshold, staircase, and tunnelling breakdown regimes. Moreover, the previous noise model's expression for the total excess noise factor in terms of ionization probabilities of the multistep staircase APD follows Friis's total noise factor. However, we demonstrate that our derived expression matches Bangera's correction to Friis's total noise factor.