D&C 107

As I ponder the teachings on the Priesthood in this section, I would like to define two words -

Standing: established by law or custom.

In my mind, "standing" would suggest position by virtue of calling.

Officiate: to perform a ceremony, function, or duty

In my mind, "officiate" would be, where granted by authority, perform duties and responsibilities.

We are taught of the Melchizedek priesthood -

"...it was called the Holy Priesthood, after the Order of the Son of God.
4 But out of respect or reverence to the name of the Supreme Being, to avoid the too frequent repetition of his name, they, the church, in ancient days, called that priesthood after Melchizedek, or the Melchizedek Priesthood."  (Doctrine and Covenants | Section 107:3 - 4)

This would suggest to me that of the Grand Priesthood, that there is an order or segment that we fall under, being an order presided over by the Son of God.  This order is His priesthood order.

And that within this order there are -

"...offices in the church..."  (Doctrine and Covenants | Section 107:5)

This order of priesthood also -

"...holds the right of presidency, and has power and authority over all the offices in the church in all ages of the world, to administer in spiritual things."  (Doctrine and Covenants | Section 107:8)

We begin to understand the purpose of this higher priesthood is to administer in "spiritual things".

Now we learn of these offices and rights within this priesthood regarding officiating -

"The Presidency of the High Priesthood, after the order of Melchizedek, have a right to officiate in all the offices in the church.
10
High priests after the order of the Melchizedek Priesthood have a right to officiate in their own standing, under the direction of the presidency, in administering spiritual things, and also in the office of an elder, priest (of the Levitical order), teacher, deacon, and member.
11 An elder has a right to officiate in his stead when the high priest is not present.
12 The high priest and elder are to administer in spiritual things, agreeable to the covenants and commandments of the church; and they have a right to officiate in all these offices of the church when there are no higher authorities present."  (Doctrine and Covenants | Section 107:9 - 12)

Note that high priests have a right to officiate in their own standing or their duty and callings.

These verses do not specifically address priesthood keys which is a topic for another days.  It only oulines standing and officiating of priesthood offices.