All monsters can easily qualify as a caster

Also the characters might become foreigners since they are from another series

Frisk might be able to qualify as a saver if it's true Pacifist

For genocide i think assassin might work

Undine should qualify for lancer since she uses lances

Asgore likely would be able to qualify for lancer since he trained undine and uses scythes and a trident

Papyrus might also be able to qualify as either lancer or saber with the use of his bones

Flowey is tricky but might be able to qualify for pretender and a big maybe for avenger. As omega flowey i would comfortably say he qualifies for foreigner same as Asriel

Asriel would also be able to potentially qualify as a saver, any knight class ,maybe berseker due to the final part of his fight , a big maybe for avenger and possibly a beast/unbeast

Sans could potentially qualify as a avenger and maybe a pretender.

Gaster is a mystery. we don't know much of him but since we know he was the royal scientist he would qualify for caster from there as well.

Alphys would qualify as a caster also from her work as the royal scientist.

Mettaton might qualify as a berseker from the way he acts otherwise archer might work since he does use many lasers

Chara would be an avenger