We propose a general framework of proper regularizationto solvenonlinear SPDEs withsingularities included in both drift and noise coefficients. As applications, the (local and global) existence is presented for a broad class of fluid models driven by pseudo-differential noise, which include the stochastic magnetohydrodynamics (hence Navier-Stokes/Euler) equations, stochastic Camassa-Holm type equations, stochastic aggregation-diffusion equation and stochastic surface quasi-geostrophic equation. Thus, some recent results derived in the literature are considerably extended in a unified way.

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