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if you are using the same plugin in the site and are willing to taker dependency on that in your source code, take a look at EPiServer.Labs.LanguageManager.Business.ILanguageBranchManager.CopyDataFromMasterBranch()
method for example (implementation is at EPiServer.Labs.LanguageManager.Business.LanguageBranchManager
). That might give you some options how to do it programmatically.
In the cms (using the Languages add-on) it is possible to create a new language version of a page and duplicate the content from another language. It is possible to do this programmatically?