Extend the Fence with Plants
While building codes don't let you build the fence taller, you can train certain plants in a way that extends the height considerably. Stiff woody vines that produce long canes can be espaliered up the fence to fan out into arches that rise well above the top. This can add two or more feet to its overall height.
Get a list of the top 10 climbing vines.
Get a list of the top 10 privacy plants.
What is a variance?
Sometimes you can petition the city to allow you to build a fence or wall taller than the code allows, but you must have a very good reason for doing so. For example, if your yard backs up to the dumpster area of a neighborhood shopping center, a larger wall helps to screen this undesirable view and reduce both noise and odor caused by the dumpster. Because petitions are considered on a case by case basis, inquire at the building or planning department of your city to see if your problem might earn a variance. Variances are not common, but can be a real benefit for problem homesites.
Vines ask for little ground space to do their job, with a single trumpet vine expanding twenty feet in each direction. This is an ideal choice for screening small spaces where there's not a square foot to spare. In cooler regions where you are limited to deciduous plants, the screen becomes transparent during the winter months.
Tradeoff: The vines will require regular training and pruning as they age to establish the proper framework. Once mature, some grow into a huge mass needing regular pruning and attention. Without pruning their growing weight can pull down the vine onto one side or the other of the fence. Fortunately once established you can hide steel pipe inside the vines to give them further support.
Tip: Some homeowners are vehemently opposed to vines, so be sure to check with your neighbor before selecting this option.