  We establish criteria on the chemotactic sensitivity $\chi$ for the
non-existence of global weak solutions (i.e. \textit{blow-up} in finite time)
to a stochastic Keller--Segel model with spatially inhomogeneous, conservative
noise on $\mathbb{R}^2$. We show that if $\chi$ is sufficiently large then
\emph{blow-up} occurs with probability $1$. In this regime our criterion agrees
with that of a deterministic Keller--Segel model with increased viscosity.
However, for $\chi$ in an intermediate regime, determined by the variance of
the initial data and the spatial correlation of the noise, we show that
\emph{blow-up} occurs with positive probability.
