Another precept for Jasher 16:11-12 Shem is Melchizedek in The Legends of the Jews by Louis Ginzberg pg. 233 or just click on "Ctrl F" and type in Melchizedek to find it quicker.
"When Abraham returned from the war, Shem, or, as he is sometimes called, Melchizedek, the king of righteousness, priest of God Most High, and king of Jerusalem, came forth to meet him with bread and wine."
"But as Shem had given it the name Shalem (Salem), Place of Peace, and TMH would not give offence to either Abraham or Shem, He united the two names, and called the city by the name Jerusalem."
Shem can't be Melchizedek. Because Shem was in the house on Noah until he died. Melchizedek was in the middle of the earth which is in Jerusalem. These are two separate locations because Melchizedek wasn't allowed to leave his place. According to other documents like "The Book of the Rolls" Goes in-depth of who is Melchizedek as Shem's great-grandson from one Shem son named Arphaxad which is the father of Malih which is Melchizedek father. Here you can read it here.
Noah lived after going out of the ship 350 years. When his death came near, there gathered to him Shem, and Ham, and Japhet, and Arphaxad, and Salah. He made vows for them, and desired the presence of Shem his firstborn, and commanded him secretly, saying to him, “When I die, bury me. Go into the Ark of safety, and take out of it the body of our father Adam secretly, let no one with thee know. Make for it a large chest, and put it within. Prepare for thyself a store of bread and
drink, and carry the chest in which is the body of our father. Take with thee Melchizedek, the son of Malih. Verily the Lord hath chosen him from the rest of your sons to minister before our father Adam. When thou reachest the centre of the earth, bury the body there, and set Melchizedek in the place for the service of the body and the praise before it. Verily the Angel of the Lord will go before you to guide you two to the place for the body, which is the centre of the earth. From it shall be seen the power of God. The four pillars of the world are joined together and have become one pillar, and from it shall be salvation to Adam and to all his children.” Thus it was written in the tables which Moses received from the hand of the Lord and broke at the time of his anger against his people. Noah strengthened Shem in receiving the testament, and told him that it was the Testament of Adam to Seth, and of Seth to Enos, and of Enos to Cainan, and of Cainan to Mahlaleel, and of Mahlaleel to Jared, and of Jared to Enoch, of Enoch to Methuselah, and of
Methuselah to Lamech, and of Lamech to Noah; he made him swear that no one [else] should attend to what he commanded in regard to the body of Adam. When he had finished his testament, he died, being 950 years old, on a Wednesday. Shem embalmed him, and with him his other children put him on a bier and buried him. They raised a wail over him for forty days. Then Shem went secretly into the ship, and took out the body of Adam. He sealed the ship with his father’s seal. Then he desired the presence of Ham and Japhet and said to them, “Know that Noah my father commanded me to journey after his death to the elevated land and to go round it to the place of the sea, that I may attend to the state of its trees, and fruits and rivers. I have already resolved on this, and have left my wife and children with you; take heed to them till the time of my return.” They said to him, “Take with thee a man since thou hast resolved on this, for the land which thou hast described has wild beasts and hunting lions.” He said to them, “Verily, the Angel of God is with me, he is my Saviour.” His brethren called to him and said, “The Lord be with thee wherever thou dwellest.” Then he said to them, “Verily, our father at his death made me swear not to enter the ship nor allow any one [else] to enter it. I have received his testament, and sealed it with his seal, and beware that ye enter it not! ye, nor any of your children.” They pledged themselves to him concerning this. Then he approached the father and mother of Melchizedek and said to them, “I wish that you would give me Melchizedek that I may journey with him in my way.” They said to him, “He is before thee, as thou wouldest journey, take him with thee.” Then Shem called Melchizedek by night, and bore with him the body of Adam secretly. They went out, the Angel going before them, till he brought them to the place with the utmost speed. He said to them, “Set him down, for this is the centre of the earth.” And they put him down from their hands. When he came to the ground, the earth was cleft for him as a door, and the body was let down into it, and they put him in it. When the body rested in its place, the earth returned and covered it over. The place was called Gumgumah, “of a skull,” because in it was placed the skull of the Father of mankind, and Gulgulah, because it was conspicuous in the earth, and was despised by its sons, for in it was the head of the hateful Dragon which seduced Adam. It was called also Otâriâ, which is, being interpreted, “the families of the world,” because to it is the gathering together of mankind. Shem said to Melchizedek son of Malih, “Know that thou art the priest of the Everlasting God, who hath chosen thee from the rest of men to minister before Him before the body of our father Adam. Accept the Lord’s choice of thee, and never leave this place. Do not marry any woman, do not shave thy hair, nor pare thy nails. Shed no blood for thyself, and sacrifice no beast. Do not build a building over this place. Let thine offerings before the Lord be of fine pure bread, and [let the] drink be of the juice of the vine. The Angel of the Lord is with thee for ever.” He wished him peace, and bade him farewell and embraced him, and returned to his dwelling. Then came to him Jozadak and Malih, the parents of Melchizedek. They asked him about him, and he told them that
he had died on the road, and that he had looked after him and buried him. His father and his people sorrowed over him with a great sorrow. When Shem the righteous was 700 years old, he died, and his son Arphaxad looked after him, and Salah and Eber, and they buried him. When Arphaxad was thirty years old, he begat Salah his son, and when he was 465 years old, he died, and Salah and Eber looked after him. They buried him in the town that Arphaxad had built, known as Arphaxad (cod. Arbalsarbat). When Salah was thirty years old, he begat Eber, and when he had completed 430 years, he died. Eber and Peleg looked after him; he was buried in the town that Salah had built, known as Salḥadîb. When Eber was thirty years old, he begat Peleg, and when he had completed 434 years, he died; his son Peleg buried him, and Reu and Serug in the town which Eber had built and had called by his name.
Then Maoalon king of Teman journeyed to Melchizedek when his fame reached him, and gave him noble and glorious presents. He honoured him when he saw him and heard his word. All kings and nations honoured him and called him the Father of Kings. Some people think that Melchizedek will not die, and bring as proof the saying of David the Prophet in his psalms, “Thou art a priest for ever after the figure of Melchizedek.” David does not wish (to say) in this his saying that he will not die, and how can this be when he is a man? But God honoured him and made him His priest, and in the Torah there is no mention of a beginning to his days. Therefore David sang as he sang about him. Moses does not make mention of him in his book, for he was only relating the genealogy of the Fathers. But Shem the son of Noah has told us in the books of the Testaments that Melchizedek was the son of Malih, son of Arphaxad, son of Shem, son of Noah; and his mother was Jozedek.
Todah for posting sister! This is great!