2 Samuel 8:18 says: "...and David's sons were priests" but of the order of Melchizedek and not Aaron, as David had declared, inspired by the Holy Spirit in Ps 110. Solomon himself offered sacrifices during the consecration of the temple [ 2 Chr 7:7 ], but Uzziah was struck with leprosy for offering incense in the Holy Place [ 2 Chr 26:16 ].
Now a few questions:
The Melchizedek priesthood is certainly not the same as the Aaronic one, and it is superior to the latter as Abraham offered tithes to the former. So thus David could eat the showbread, and even share it with his companions, and Solomon can offer sacrifices. But why was Uzziah struck with leprosy? Thus there are restrictions in the Melchizedek priesthood even as with the Aaronic one, such as David and his companions being chaste before consuming the showbread, but Uzziah was "arrogant". How can we figure out what is the difference between these two priesthoods? Certainly the author of Hebrews understood them. How?
Is there any way of knowing how the ancient Israelites themselves understood Ps 110? In the days of David and his sons? In the time of Jesus? Of the Essenes?
Is the covenant of salt [ 2 Chr 13:5 ] related to the Melchizedek priesthood?
Were there other Melchizedek priests in other parts of the world at various times until Christ appeared? Perhaps Balaam was such a priest that have gone bad. And I've seen suggestion that Jethro, the Midanite, Moses' father-in-law was one too, and even Joseph when he was serving the Pharaoh. Is there anything in the order that forbids such other instances of the priesthood?