If you do not find anything more automated, here is a workaround solution that will work at least for .srt files:

You can use Nikolaj Lynge Olsson's Subtitle Edit to first adjust each file individually to the video - you do not have to do this line by line; for each file, just pick one of the first lines and one of the last lines and manually adjust their time of appearance and duration. Subtitle Edit can then adjust the rest of the file for you.

Once that is done, you can use the Tools -> Append subtitle command to join all files in Subtitle Edit and save them as a complete subtitle file.

I am not affiliated with that project. However, I have often used the program for synching subtitles with little effort.

If you do not find anything more automated, here is a workaround solution that will work at least for .srt files:

You can use Nikolaj Lynge Olsson's Subtitle Edit to first adjust each file individually to the video - you do not have to do this line by line; for each file, just pick one of the first lines and one of the last lines and manually adjust their time of appearance and duration. Subtitle Edit can then adjust the rest of the file for you.

Once that is done, you can use the Tools -> Append subtitle command to join all files in Subtitle Edit and save them as a complete subtitle file.

I am not affiliated with that project. However, I have often used the program for syncing subtitles with little effort.