Historical text normalization suffers fromsmall datasets that exhibit high variance,and previous work has shown that multitasklearning can be used to leverage datafrom related problems in order to obtainmore robust models. Previous work hasbeen limited to datasets from a specific languageand a specific historical period, andit is not clear whether results generalize. Ittherefore remains an open problem, whenhistorical text normalization benefits frommulti-task learning. We explore the benefitsof multi-task learning across 10 differentdatasets, representing different languagesand periods. Our main finding—contrary to what has been observed forother NLP tasks—is that multi-task learningmainly works when target task data isvery scarce.