How many Quorums of Seventy are there?

[Hemidakota]

Not right now...there is a permanent seventies quorum and a five-year calling quorum.

[Hemidakota]

Sidenote for future callings that will enlarge the Seventies:

D&C 77:11 Q. What are we to understand by sealing the one hundred and forty-four thousand, out of all the tribes of Israel--twelve thousand out of every tribe?

A. We are to understand that those who are sealed are high priests, ordained unto the holy order of God, to administer the everlasting gospel; for they are they who are ordained out of every nation, kindred, tongue, and people, by the angels to whom is given power over the nations of the earth, to bring as many as will come to the church of the Firstborn.

If you look closer, you find these are Seventies. I do assume since the Prophet Joseph Smith is the head of this dispensation, it will be under his hand to ensure that all are called for Christ [prior to his death and afterwards] - as His standing missionary army. I will also assume, those living in Morality will be visited by JS for more instruction prior to their calling.

7. At this time Joseph Smith was not willing to discuss the temple ordinances of conferral of the fulness of the priesthood, of marriage for time and eternity, or of sealing children to parents; nevertheless, he indicated that the conferral of the fulness of the priesthood was a "sealingon top of the head", of which the phrase "sealed in their foreheads" was symbolic. Furthermore, Joseph Smith here taught that it was through the ordinance of conferral of the fulness of the priesthood that men could be qualified to be a part of the special missionary force of the last days which would number 144,000 high priests (D&C 77:8-11, 14). When Cornelius P. Lott and his wife received these ordinances on 4 February 1844, the Prophet indicated that "the selection of the persons to form that number had already commenced." He had already conferred these blessings on at least 17 men (History of the Church, 6:196 and Wilford Woodruff Diary, under date given).

(Joseph Smith, The Words of Joseph Smith: The Contemporary Accounts of the Nauvoo Discourses of the Prophet Joseph, compiled and edited by Andrew F. Ehat and Lyndon W. Cook, p.297)

As Elder Lund pointed out:

2. The Prophet clearly indicates that the twelve thousand sealed from each of the twelve tribes is not just a symbolic representation of the forces of righteousness, as some scholars maintain. They are a great missionary force of the sixth seal (see D&C 77:10). Joseph Smith shows us that they are ordained high priests chosen from among every nation to carry forth the gospel and bring as many as will come to the true Church (see D&C 77:11). In another revelation the Prophet indicated that these 144,000 would also stand on Mt. Zion with the Savior (see D&C 133:18 and compare with Rev. 14:1-5).

The Prophet also said, shortly before his death, "I attended prayer-meeting with the quorum in the assembly room, and made some remarks respecting the hundred and forty-four thousand mentioned by John the Revelator, showing that the selection of persons to form that number had already commenced."32 This statement would seem to indicate that this great body of missionaries may be composed of mortals and immortals together. (Gerald N. Lund, Selected Writings of Gerald N. Lund: Gospel Scholars Series , p.91-92)