  In this paper we focus on nonlinear SPDEs with singularities included in both
drift and noise coefficients, for which the Gelfand-triple argument developed
for (local) monotone SPDEs turns out to be invalid. We propose a general
framework of \emph{proper regularization} to solve such singular SPDEs. As
applications, the (local and global) existence is presented for a broad class
of fluid models driven by pseudo-differential noise of arbitrary order, 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.
