The Sanskrit word Parampara (literally, uninterrupted series of succession) refers to the process of succession inside an established Sampradaya, sect or tradition. The succession of parampara is a strict succession. There is never more than one active master at the same time in the same guruparamaparya (lineage).
In most Guru Sampradayas, the selection of a successor is based on an appraisal of the disciples by the Guru. The selection of the most qualified disciple is made as an act of Will to ensure the continuity of the line. The process of paramapara is finalized upon the death of the former Sampradaya Guru.
Within the International Nath Order that strict seat is not what is being offered. Shri Gurudev Mahendranath was the last guru of the Adinath and Uttara Kaula sadhu sects; those householder-excluding lines were not to continue through the West. What continues is the Nath initiation he established for the Order, now tended under Sri Kapilnath, Imperator Magus Mundi. Several chartered Initiators may give that diksha. That is not a second sampradaya throne. The names of the line are on the Lineage page. How initiation is asked for is not defined here.