I actually was thinking Yiddish as a big language but it was already pointed out that has already happened. Also a Prussian language splitting off from German. And the Czech languages (Czech, Slovak, Moravian, etc) merging or staying as a single language if Bohemia managed to stay independent from Austria and grow into a local central eastern power. And a sort of Gaelic language appearing in the Americas (similar to how Afrikaans split from Dutch). POD is about 500 years ago.
Would this Prussian be a survival of the old Baltic language or a dialect of German that grew up in the area. The second actually happened in OTL, a Low German dialect called Low Prussian
Don't know enough to say about Bohemian. Presumably the dialect of Prague would become the standard and Moravian and Slovak would regarded as country dialects and could disappear.
As for an American Gaelic it sort of happened in OTL too: Canadian Gaelic