Hi John, that's a tricky one... What species or hybrid are you talking about? Dormancy can be a bit different for different individuals in this section.
I had a similar situation last fall (N. Hemisphere fall, that is) with an alba Den. nobile that was starting several new canes just when I thought it should go dormant.
I did some reading and came up with a plan of action: Throughout the fall and winter I withheld ferts entirely, gave it temps ~ 13 C at night and 18 C daytime, high light and reduced but not eliminated water. Actually, that's pretty much how I treated all my Dens of this type.
Anyway, the new growths slowed down a lot but kept growing during this dormant period. I gave the plant to my Dad about a month and a half ago so I haven't been monitoring it closely, but it seems like they picked up and started rapid growth again once temperatures warmed up.
Two of the mature canes that still had their leaves bloomed very nicely late in the winter, though they went one after another rather than blooming at the same time.
Your mileage may vary, but I'd say you could probably just go with your usual winter routine for this one. Hope this helps!
--Nat