  State-of-the-art machine translation (MT) systems are typically trained to
generate the "standard" target language; however, many languages have multiple
varieties (regional varieties, dialects, sociolects, non-native varieties) that
are different from the standard language. Such varieties are often
low-resource, and hence do not benefit from contemporary NLP solutions, MT
included. We propose a general framework to rapidly adapt MT systems to
generate language varieties that are close to, but different from, the standard
target language, using no parallel (source--variety) data. This also includes
adaptation of MT systems to low-resource typologically-related target
languages. We experiment with adapting an English--Russian MT system to
generate Ukrainian and Belarusian, an English--Norwegian Bokm{\aa}l system to
generate Nynorsk, and an English--Arabic system to generate four Arabic
dialects, obtaining significant improvements over competitive baselines.
