Can the HVAC system allow for different temperatures in different parts of the house?
With a properly designed zoning system ,yes.
You can also do it to some extent with manual dampers or closing the grille partially in some rooms/
What is you goal,temperature difference and for what % of the home??
We would like the main part of the house to remain at 20 degrees, and we would like the 1 bedroom addition to be at 23 degrees approx.
If you are only wanting to keep one room warmer than the rest of the house, you need to look at using a space heater of some type.
If more government is the answer, then it's a really stupid question.
I agree with Mark, put in some form of space heating, it would be the easiest most cost effective and easiest to install.
"Go big or Go Home"