  We contribute to the classification of modular categories $\mathcal{C}$ with
$\operatorname{FPdim}(\mathcal{C})\equiv 2 \pmod 4$. We prove that such
categories have group of invertibles of even order, and that they factorize as
$\mathcal C\cong \widetilde{\mathcal C} \boxtimes \operatorname{sem}$, where
$\widetilde{\mathcal C}$ is an odd-dimensional modular category and
$\operatorname{sem}$ is the rank 2 pointed modular category. This reduces the
classification of these categories to the classification of odd-dimensional
modular categories. It follows that modular categories $\mathcal C$ with
$\operatorname{FPdim}(\mathcal{C})\equiv 2 \pmod 4$ of rank up to 46 are
pointed. More generally, we prove that if $\mathcal C$ is a weakly integral MTC
and $p$ is an odd prime dividing the order of the group of invertibles that has
multiplicity one in $\operatorname{FPdim}(\mathcal C)$, then we have a
factorization $\mathcal C \cong \widetilde{\mathcal C} \boxtimes
\operatorname{Vec}_{\mathbb Z_p}^{\chi},$ for $\widetilde{\mathcal C}$ an MTC
with dimension not divisible by $p$.
