Because the home's top and bottom are already balanced by the foyer, adding on to one side or the other will make your home look lopsided. For that reason, any home addition ideas involving extending one side should include an extension to the other. The length of your home on each side of the split foyer should be approximately equal in length. This can be challenging if you just want to add a bedroom or two, but you can add a garage and a workroom (lower and upper levels, respectively) to maintain the balance on the other end with minimal expense. Other ideas are building a large sun room, or adding a great room with a two-story ceiling.
If you can't afford to pay for two new sections on your home, your addition should be in the back. Keep it as close to the center as possible; even though it won't face the road, you still want the back of your home to balance. If you must build it off-center, build a deck, a sun room or a similar outdoor-oriented structure to balance it on the other side.
Since many split-foyer homes are built to take advantage of a sloping lot, you may be unable to adequately balance your addition due to an inconvenient hill or ridge. In that case, balance it with landscaping. Build your bedroom in the spot where it needs to be, then plant tidy bushes in front of it, or plant trees on the other side to balance it. If you decide to go this way with your split-foyer home addition, you should consult with a professional landscaper to examine your options and find out what would blend best with your plans.
There are some good ways to expand your split-foyer home without building onto it. The most common one is the garage conversion. Most split-level and split-foyer homes are based on a home plan that includes a garage, and the garage is often generous in proportions. A two-and-a-half-car garage, for example, can be converted into two bedrooms and a sitting room with some drywall, carpeting and ventilation, or you can make it into a handy game room, teen hangout, home theater or large playroom for your children.
This leaves you without a garage, but the solution to that may be building a small detached garage or a carport, both of which are easier to balance with a split-foyer home than a new addition is. A detached garage also allows for more planning flexibility, enabling you to include a workshop or other desirable space as well.
If you're crazy about your split-foyer home and have money to burn, you can get really creative. Split-foyer homes are notoriously boring in appearance, boxy with short eaves and often no real external features. Consider changing the focal point of your home exterior from the oddly placed entry door to something else: graceful antebellum columns supporting a new porch roof, for instance, or a wraparound porch under newly extended roof eaves. Or build a faux or real tower on either end, and you have the core of a modern Victorian-looking home or a small Tudor castle.
The advantage of this sort of creative change is that it enables you to get away with almost anything, because that delicate balance is no longer necessary. Your home, with a new focal point, no longer depends on that front door's placement. The disadvantage, of course, is that it's considerably more expensive than most other home additions.