Just 'unpack' the terminology and then re-apply it to your question.
The 'mediant' just means that the roots of the two chords are separated by a third. Starting from a tonic chord the other chord root found at a third ascending or descending is either the mediant or the submediant. Those two labels are just collapsed - for convenience - into one term mediant to mean two chord roots separated by a third.
The 'chromatic' just indicates something about the second chord is chromatically altered, either the root is lowered/raised (along with the fifth) or the third of the chord is lowered/raised.
You can apply the same idea but change mediant to another tone. For example, if we coin the term chromatic second or chromatic supertonic we could go from the
ii in major and then make our chromatic alterations: lower the root and fifth to get a
bII chord or raise the third and get a
II chord. But, those two chords already have identities as the
V/V chords respectively.
If we go from
V and explore the same possibilities for a hypothetical chromatic dominant, we get...
- lower the root and fifth: not a triad
- raise the root and fifth:
#v or enharmonically
- lower the third:
v minor dominant, Mixolydian flavor
- raise the third: not a triad
With the lowered third we get something already familiar.
With raising the root/fifth we get something different, something that really should not get any labeling as a dominant.
The other two are non-tertian.
But why isn't there talk of chromatic seconds, or fourths, or fifths, or other intervals apart from thirds?
You can explore questions like this and see where they lead.
Mostly these chords will be borrowed chords or secondary dominants, but there may be some novel things to explore.