  Phonon-driven $s$-wave superconductivity is fundamentally antagonistic to
uniform magnetism, and field-induced suppression of the critical temperature is
one of its canonical signatures. Examples of the opposite are unique and
require fortuitous cancellations and very fine parameter tuning. The recently
discovered Ising superconductors violate this rule: an external magnetic field
applied in a certain direction does not suppress superconductivity in an ideal,
impurity-free material. We propose a simple and experimentally accessible
system where the effects of spin-conserving and spin-flip scattering can be
studied in a controlled way, namely NbSe$_2$ monolayers dosed with magnetic
$3d$ atoms. We predict that the critical temperature is slightly increased by
an in-plane magnetic field in NbSe$_2$ dosed with Cr. Due to the band spin
splitting, magnetic spin-flip scattering requires a finite momentum transfer,
while spin-conserving scattering does not. If the magnetic anisotropy is
easy-axis, an in-plane field reorients the impurity spins and transforms
spin-conserving scattering into spin-flip. The critical temperature is enhanced
if the induced magnetization of NbSe$_2$ has a substantial long-range
component, as is the case for Cr ions.
