Please support the iTunes variant extension "M4P".

Great product! I have sent a donation to Florian.

Many of my downloads from iTunes to my Windows machine come with the extension 'M4P' instead of 'MP4'. The file format, as near as I can tell, is the same, but I think the M4P extension is Apple's way of tricking Windows to use the iTunes player. Anyway, in order to use MP3TAG on these files I have to change their extension to MP4. I own another product that does this in bulk, but it would be nice if MP3TAG could just read these files directly. Thanks!

Go to Tools>Options>Tags
and add the file-extension in question into the list of files to include.

Isn't the *.m4p filetype a "protected" version of the *.m4a filetype?
See dialog "Mp3tag\Options\Tags" ...
you may add the *.m4p filetype to the list of displayed filetypes ...
and try out, how Mp3tag can handle this type of "apple file".

DD.20150624.1911.CEST

Thanks for your help, friends. I didn't see the Option/Tags dialog in my quick look through the Help. I guess I should RTFM. I think I'll need to change M4P to MP4 , because some other audio software I use doesn't recognize M4P.

If you do this Mp3Tag is able to show files with the m4p-suffix but you cannot write tags to these files.

This would be interesting: as teh m4p-type is not supported natively, any added extension is treated as "not known" - but if it is a known extension (i.e. rename the file), MP3tag tries to open it with the algorithm for that particular file extension.
I wrote a thread in the German section
/t/16918/1
that described MP3tag's behaviour: if you modify an extension from e.g. mp3 to flac, you see no tags as apparentyl flac tags are expected. Any attempt to write flac tags then fails.

Coming back to the original post: if MP3tag can read the tags after the m4p file has been renamed to mp4 then the situation is different as the OP is quite right: the extension m4p should be added to the known extensions and the tag-reading done accordingly.

Or the internal computing in MP3tag has to be changed to read the file data instead of relying only on the correctness of the extension in the filename.

As the OP found that other programs cannot cope with m4p as well and he found a workaround, it looks to me as though it is not a pressing problem.

Yes, I have expected this result.
Another check would be ... to rename the file extension from "m4p" to "m4a".

DD.20150625.0810.CEST

This is why I like MP3. It works with everything.