In this paper we extend recent theoretical results on the structure of the probability density function of streamflows forced by stochastic rainfall sequences. Our extension is aimed at incorporating an additional, independent source of variability assumed to describe noisy constitutive storage-discharge relations, thought of as portraying phenomena like transient connectivity, differential activation of preferential flow paths, or macroscopic effects of spatially heterogeneous and hysteretic subsurface properties. We first show by numerical simulation that a colored noise superposed to the storage-discharge relation does not appreciably affect the overall characterization of the storage distribution. Streamflows prove more sensitive to such noise. This effect is examined by including stochasticity directly into the streamflow generation processes in the form of Gaussian multiplicative noise affecting the discharge equation of a linear reservoir. Under the above conditions, exact analytical probability distributions for the streamflow are derived. The results show that the streamflow regimes, roughly termed wet and dry to describe perennial or ephemeral streamflow regimes, are peculiarly modified by the noise and are controlled by the ratio between the subsubsurface percolation frequency, by the inverse of the mean residence time of subsurface flow, and by the noise strength. Our results suggest new and significant noise-induced phenomena, with notable ecological implications in particular for possible shifts from perennial to ephemeral regimes.