I have two butterfly bushes. One is the conventional multistalk type which I cut back annually and it does well. The other is a single stalk
There are a number of species and cultivars of the Buddleja genus. The common one is Buddleia davidii which is commonly referred to a the Butterfly Bush. These are hardy in the Philadelphia area and zones 6-9. Most of the plants in the genus are shrubs, some blooming on last year's growth, but most bloom on this year's growth.
Shrub Buddleias that bloom on this year growth in summer and autumn are cut back drastically annually in spring when the buds begn to swell. They can be cut back again after the first bloom is over, but not as drastically. This promotes subsequent blooms.
Shrub Buddleias that bloom in spring or early summer on last year's growth are pruned after bloom, cutting out about 1/3rd of the shoots to the base to promote replacement growth. Other branches that bloomed can be cut back selectively to nodes where branching occurs.
Tree Buddleias are infrequent, but are cut back to within 2-4 buds of the permanent framework. This is done in spring for those that bloom on last year's growth and after bloom on those that bloom on current year's growth.