There is a limit to what you can do but some reductions can be accomplished as well as some thinning of dense foliage.

The main thing to keep in mind is that boxwoods do not reliably regenerate from bare wood, so don't prune back beyond where leaves are growing on any branches. Generally, cutting about 3/4 of the way into the leaves is as far as you want to go. If you begin to shape the plant so that the top is narrower than the base, the lower leaves will get more light and you may get some additional, minor growth towards the bottom. You should also think about thinning the dense growth to allow more light to penetrate the plants so the bare parts are not as extensive.

Information on the various types of pruning of boxwoods are on the first page of our Guide to Boxwood. It will help you time the reduction for the best health of the plants and includes information on general care, soil improvement and nutrition to support the plants while they recover from the haircut. 

Courtesy of NYBG Plant Information Service