Arnorian successor states? 3 or more

[Belegorn]

After Eärendur passed away Arnor broke into 3 kingdoms held by his sons. The eldest held sway in Arthedain and this line continued whereas the line of Amlaith's brothers perished.

Originally Posted by Appendix A: The North-kingdom and the Dúnedain

the line soon perished in Cardolan and Rhudaur.

By the time of Argeleb [1226-1356 T.A.] there were no other descendants of Isildur in the other two kingdoms. It was due to this that they started reclaiming lordship of Arnor and this accounts for the Ar- prefix in their names since then.

Originally Posted by Appendix A: The North-kingdom and the Dúnedain

the kings of Arthedain again claimed the lordship of all Arnor... since no descendants of Isildur remained in the other kingdoms

There were still Dúnedain in those other kingdoms even when the other descendants of Isildur perished. They did perish in Cardolan in 1636 after the Great Plague hit them.

To your question, it would seem there were no other lesser kingdoms. When lesser kingdoms is mentioned in the text I think it refers to the 3 lesser kingdoms that formed after Arnor broke apart, "The sons of the king established smaller independent kingdoms." [Heirs of Elendil; The Northern line of Arnor: the Isildurioni] They were lesser kingdoms all than Arnor. Chief of those lesser kingdoms [Arthedain, Cardolan, and Rhudaur] were "Cardolan south of the Great Road and east of the Baranduin; and Rhudaur north of the Great Road between the Weather Hills and the Bruinen."