  We prove the existence and uniqueness of probabilistically strong solutions
to stochastic porous media equations driven by time-dependent multiplicative
noise on a general measure space $(E, \mathscr{B}(E), \mu)$, and the Laplacian
replaced by a self-adjoint operator $L$. In the case of Lipschitz
nonlinearities $\Psi$, we in particular generalize previous results for open
$E\subset \mathbb{R}^d$ and $L\!\!=$Laplacian to fractional Laplacians. We also
generalize known results on general measure spaces, where we succeeded in
dropping the transience assumption on $L$, in extending the set of allowed
initial data and in avoiding the restriction to superlinear behavior of $\Psi$
at infinity for $L^2(\mu)$-initial data.
