  In this paper, we establish the large deviation principles for stochastic
porous media equations driven by time-dependent multiplicative noise on
$\sigma$-finite measure space $(E,\mathcal{B}(E),\mu)$, and the Laplacian
replaced by a negative definite self-adjoint operator. The coefficient is only
assumed to satisfy the increasing Lipschitz nonlinearity assumption without the
restrictions to its monotone behavior at infinity for $L^2(\mu)$-initial data
or compact embeddings in the associated Gelfand triple. Applications include
fractional powers of the Laplacian, i.e. $L=-(-\Delta)^\alpha,\
\alpha\in(0,1]$, generalized $\rm Schr\ddot{o}dinger$ operators, i.e.
$L=\Delta+2\frac{\nabla \rho}{\rho}\cdot\nabla$, and Laplacians on fractals.
