The lack of reaction to the quesion seems to suggest that it doesn't exist!

If you look at the basic structure of melodrama, the characters are very two-dimensional: the villain is perpetually wicked, a corrupter of morals, with no redeming features.  The heroine is always innocent and pure (with no redeming wickedness!)  If you try to put that into a modern context, it would come over as corny, so I think there is an inherent contradiction in the question.

Consequently, modern melodramas (by which I mean recently written ones) tend to be set in the Victorian era (Victorian to me - I'm English), and tend to be send-ups of the genre, with the characters caricatured.  (See, for example, The Horrible Hot-Air Homicide.)

What modern topics would you expect to be tackled by melodrama?

Delia Dancer, Doughnut Girl
www.hitplays.com
This is a "moden melodrama"
Good luck