Does the Hofmann Rearrangement extend to Secondary Amides?
I think it's not possible, because if you go through the reaction mechanism, you will see that in the 1st and 3rd step two protons are needed to be abstracted by the base to proceed the reaction. So if you take a secondary amide, i.e., one of the H being substituted by any alkyl/acyl/aryl group, the base will not be able to abstract that group and hence the reaction will not progress to any fruitful product. 



Pic reference: http://www.name-reaction.com/hofmann-rearrangement