The noise-flatness-induced hypersensitive transport of overdamped Brownian particles in a tilted ratchet system driven by multiplicative nonequilibrium three-level Markovian noise and additive white noise is considered. At low temperatures, the enhancement of current is very sensitive to the applied small static tilting force. It is established that the enhancement of mobility depends nonmonotonically on the parameters (flatness, correlation time) of multiplicative noise. The optimal values of noise parameters maximizing the mobility are found.