Second album cover

When I upload music from mp3tag to apple music, I want some songs to have a different cover art to appear next to the song name when you play them. But right now the albums main cover always overrides it and I have no idea how to get other album artwork to show. Does anyone know how I can do this?

For test purposes, you could delete the unwanted picture and see whether your player shows the embedded picture or something else.
And then you could test if if matters what kind of cover type you assign like the player always takes "Front" as main picture. Then it may be a way to change the cover type of the unwanted picture to something other than "front".

It didn't seem to matter what cover type I used, it kept happening every time. Below I uploaded an image of what I'm looking for. I found that it works If I have a different image for each song (because it takes the cover of the first song as the album cover by default), but thats not very effective because I want the first song to have a separate cover too.

iTunes will only display the first cover art tagged on any song, no matter how many you have in each tag, or what title you have applied. This is a limitation in the player software. It is not able to display anything different when playing. It will show the addtional art if you show the individual track details (Ctrl+I). So the info is there, just no way to manipulate it during playback.

This is not limited to iTunes by the way. There are only a few players today able to display anything more than the first cover.

That makes sense. The thing is though you can have each track display a different cover, but that only works if you want the cover of the first track to be the cover for the whole album (because the album cover defaults to the cover of the first track). I just wish there was a way to change what the albums cover art defaults too, or upload a separate file that it could read as the cover of the album.

and also changing it through Album info>Add artwork on itunes doesn't work either because it then replaces all the songs cover art with that image.

That is correct. ITunes has no way of working with more than a single cover. I wouldn't expect that to change at this point.

It is much easier to manage separately with mp3tag. Use a script to force iTunes to update after any mass track changes if they are already in your iTunes library.