Is there more than one High Priest in the order of Melchizedek?

The Church of Jesus Christ of Latter-day Saints believe that the priesthood, both Aaronic/Levitical and Melchizedek, have been restored by Joseph Smith in 1829.

The word priesthood has two meanings. First, priesthood is the power and authority of God. It has always existed and will continue to exist without end. Through the priesthood, God created and governs the heavens and the earth. Through this power, He exalts His obedient children, bringing to pass “the immortality and eternal life of man”.

Second, in mortality, priesthood is the power and authority that God gives to man to act in all things necessary for the salvation of God’s children. The blessings of the priesthood are available to all who receive the gospel.

The offices of the Melchizedek Priesthood are Apostle, Seventy, patriarch, high priest, and elder. The President of the High Priesthood is the President of the Church

On the office of high priest

High priest is an office of the Melchizedek Priesthood. A high priest has the right to officiate in the Church. Stake presidents, mission presidents, high councilors, bishops and their counselors, and other leaders of the Church are ordained as high priests.

Summary: Yes there are new high priests here on earth. There can be multiple high priests and multiple Melchizedek priesthood holders (they are not necessarily synonymous-an elder who holds the Melchizedek priesthood is not a high priest).

The priesthood of Melchizedek was unique, because Melchizedek was unique - a one-off. It should not be surprising, therefore, that when God speaks of Christ as being priest forever in the order of Melchizedek (Hebrews 4:14 to 5:10), this is a unique, one-off matter.

Before drawing parallels between Melchizedek and Christ, here are a few quotes from Reformed Protestant sources as to its stance on priesthood, as an office in the Christian church, which will provide a foundation for grasping its conclusions on how many there might be in the priesthood order of Melchizedek.

"An alien concept is... the assigning to ministers a mediatorial work as priests. Scripture asserts that Christians as a whole constitute a priesthood (1 Pet.2:5). Scholars are agreed that a sacerdotal ministry does not appear in Christian writers until the close of the second century. 'Sacrifice is no part of the Christian ministry' (Hooker)." (In Understanding Be Men, p1612, T.C. Hammond, Inter-Varsity 1997 ed.)

Reformed Protestants are keen to point out the significance of Christ not being in the Aaronic priesthood, which came much later on than that of Melchizedek. This is expanded on in the notes in the NIV Study Bible, regarding Hebrews 6:20 to the end of chapter 8 where the ministries of Melchizedek and Christ are compared.

"Of particular significance is Melchizedek's holding both offices - king and priest [Heb.7:1-10], one of the ways in which he prefigures Christ... King of righteousness, king of peace, are Messianic titles (see Isa.9:6-7; Jer.23:5-6; 33:15-16).

'Without father, or end of life - Gen.14:18-20, contrary to the practice elsewhere in the early chapters of Genesis, does not mention Melchizedek's parentage and children, or his birth an death. That he was a real, historical figure is clear, but the author of Hebrews (in accordance with Jewish interpretation) uses the silence of Scripture about Melchizedek's genealogy to portray him as a prefiguration of Christ. Melchizedek's priesthood anticipates Christ's eternal existence and his unending priesthood." (NIV Study Bible, p1825)

The Study Notes then go on to show how Melchizedek was greater than Abraham, and that his priesthood was in effect before the Mosaic law was given. But with the Aaronic priesthood, the law was integral to that. Heb.7:11-17 expressly states:

"If perfection could have been attained through the Levitical priesthood (for on the basis of it the law was given to the people), why was there still need for another priest to come - one in the order of Melchizedek, not in the order of Aaron? ...For it is clear that our Lord descended from Judah, and in regard to that tribe Moses wrote nothing about priests, And what we have said is even more clear if another priest like Melchizedek appears, one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life."

The NIV Study Bible notes point out that the Aaronic priesthood was imperfect, but Melchizedek's was perfect:

"The announcement of the coming one who would be a priest for ever (Ps.110:4) was written halfway through the history of the Levitical priesthood, which could only mean that the existing system was to give way to something better, for that one to come is priest for ever"... Jesus is a perfect high priest for ever; so he is able to save completely and for all time. His people will never be weithout a priestly representative (see Jn.17; 1 Jn.2:1)." (Ibid. p1826)

This means that although the Bible does speak of Christians reigning with Christ as priests and kings (Rev. 7:9-15 & 20:4-6), it is neither in the order of Aaron nor of Melchizedek. That is because the Aaronic priesthood passed away with Christ's supreme, once-for-all-time perfect sacrifice of himself as the great high priest in the order of Melchizedek. Because Melchizedek was only one, and Christ is only one, their unique status means no other humans can approach that ministry. Christ alone carried it out. No more sacrifices are needed. This is confirmed in this final quote:

"The New Testament attributes Jesus' appointment as High Priest to a higher order than the one prescribed under the old covenant: namely, the Melchizedek priesthood, after the priest-king whom Abram recognized as his superior in Genesis 14:18-20 long before the giving of the law and therefore long before the Aaronic priesthood... This makes Jesus the guarantor of a better covenant - Heb. 7:18-22. Thus, priesthood and covenant are inextricably connected; a change in one requires a change in the other. Or rather, since covenants cannot be amended, an inferior one must become 'obsolete' in the inauguration of the superior one (Heb.8:13). Christ's priesthood is therefore not grounded in history, but in eternity; not at Sinai, but in the heavenly Zion." (Pilgrim Theology, pp186-7, Michael Horton, Zondervan 2011)

Summary of Answer: Christ alone is the one great High Priest in the order of Melchizedek. This priesthood is uniquely fulfilled in Christ, with no other literal priestly system on earth since his perfect sacrifice, let alone any re-enactment of sacrifices since then, or men claiming to continue Aaronic/Levitical positions. The role of Christians as stated in Revelation 1:6 is a spiritual function, all members of the Christian church being such ones designated as kings and priests unto God. This is spiritual, not literal. All members of the Christian church are "one in Christ Jesus", without distinction as shown in Gal.3:28 & Col.3:11.

The nature of the office of Highpriest prohibits the existence of more than one high priest at any point of time.

We find that the succession of the Highpriest occurs at the death of the current highpriest.

Num 20:24-28 Aaron shall be gathered unto his people: for he shall not enter into the land which I have given unto the children of Israel, because ye rebelled against my word at the water of Meribah. Take Aaron and Eleazar his son, and bring them up unto mount Hor: And strip Aaron of his garments, and put them upon Eleazar his son: and Aaron shall be gathered unto his people, and shall die there. And Moses did as the LORD commanded: and they went up into mount Hor in the sight of all the congregation. And Moses stripped Aaron of his garments, and put them upon Eleazar his son; and Aaron died there in the top of the mount: and Moses and Eleazar came down from the mount.

So at no point, there were 2 highpriests.

Also note that Melchizedek is called the "priest of the Most High God", not "High Priest".

Gen 14:18 And Melchizedek king of Salem brought forth bread and wine: and he was the priest of the most high God.

The order of Melchizedek is simply used to denote that the coming High Priest is both a king and a priest at the same time which was strictly forbidden under the Levitical priesthood.

There has only been one high priest in this order of Melchizedek - and there will be no succession because Christ ever liveth to make intercession for His people.

Heb 7:25 Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.

God also said explicitly:

Ps 110:4 The LORD hath sworn, and will not repent, Thou art a priest for ever after the order of Melchizedek.

Christ is a high priest forever, that is until the office shall last.

Note: There are other priests in the order of Melchizedek, but only one high priest.

Rev 1:5 And from Jesus Christ, who is the faithful witness, and the first begotten of the dead, and the prince of the kings of the earth. Unto him that loved us, and washed us from our sins in his own blood, Rev 1:6 And hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen.