  We investigate the vacuum stability as well as the gravitational corrections
in extensions of the Standard Model featuring a new complex scalar, and two
Dirac fermions for different choices of the hypercharge of the scalar and one
of the two fermions. The neutral fermion acquires loop-induced magnetic
interactions with the Standard Model and could be identified with a dark matter
candidate. To the lowest order in perturbation theory we show that these
extensions can save the electroweak vacuum from being metastable. We then add
the gravitational corrections to the different beta functions and discover that
the models can be compatible with the asymptotically safe gravity scenario at
the price of a heavier Higgs and lighter top mass.
