[Belegorn]

In Of the Rings of Power and the Thrid Age it is said of Arnor after the passing of Elendil that "of the Númenóreans and of the Men of Eriador there remained now too few to people the land or to maintain all the places that Elendil had built". This may be useful for your question of the possibility of more than three kingdoms. The kingdoms were taken out one by one, as they diminished due to infighting and of course war with Angmar. I do not know if Arthedain was the greatest of these three realms, but its royal line was maintained where it faded away in the other two, as well as the line of princes in the other kingdoms. The other two kingdoms did fade in their strength faster than Arthedain which is why it was pointed out that Argeleb l was slain in battle with the subkingdoms. During his time the royal line was not existent in the other two kingdoms anymore and perhaps those two kingdoms did take a hit with their passing.