Japan has embraced UTF-8, and before that they embraced Shift-JIS - a homegrown encoding that also didn't support constructing new characters. Is there any encoding that works well for this particular case? AFAIK there aren't any of any prominence, which suggests that it's a non-issue - surely if constructing new characters was important to them, Japanese or Chinese or Taiwanese computer scientists and standards organizations would push for some kind of encoding that enabled it.