DESIRE : Strong’s Greek 1937 : LONG, To long for, covet, lust after, set the heart upon. From  epi and thumos; to set the heart upon.

MANIFOLD : Strong’s Greek 4164 : MANY COLORED. Usage: various, of different colors, diverse, various.

UTTERMOST : Strong’s Greek 3838 : Complete, entire, perfect, through all time.  From pas and telos; full-ended

“Show hospitality to one another without complaining.  As good stewards of the MANIFOLD GRACE of God, each of you should use whatever gift he has received to serve one another.  Of this salvation the prophets have inquired and searched carefully, who prophesied of the GRACE that would come to you, searching what, or what manner of time, the Spirit of Christ who was in them was indicating when He testified beforehand the sufferings of Christ and the GLORIES that would follow.  To them it was revealed that, not to themselves, but to us they were ministering the things which now have been reported to you through those who have preached the gospel to you by the Holy Spirit sent from heaven — things which angels DESIRE to look into. (see commentaries below)   1 Peter 4:9-12.

“But blessed are your eyes because they see, and your ears because they hear.  For truly I tell you, many prophets and righteous men longed to see what you see but did not see it, and to hear what you hear but did not hear it.”   Matthew 13:16-17.

“Then Jesus turned to the disciples and said privately, “Blessed are the eyes that see what you see.  For I tell you that many prophets and kings desired to see what you see but did not see it, and to hear what you hear but did not hear it.”   Luke 10:23 -24 BSB.

“AThen was fulfilled what was spoken by the prophet who said, “I took THIRTY silver coins, the price of The Precious One on which they of the children of Israel had agreed.”   Matthew 27:9 Aramaic Bible in Plain English.

“For the kingdom of God is not a matter of eating and drinking, but of righteousness, peace, and joy in the Holy Spirit.”   Romans 14:17.

“These all died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth,”   Hebrews 11:39.

“Wherefore also He is able to save to the uttermost those drawing near to God through Him, always living for to intercede for them.”   Hebrews 7:25.

“For by one Offering He has perfected forever those who are being sanctified.”   Hebrews 10:14.

Ellicott Commentary : 1 Peter 1:10 : “Do I say that prophets, who had the mysteries of our redemption on their lips, yet pored in vain to catch the detailed meaning which you catch?  Nay; angels (not “the angels”), who were present at every detail, and bore an active part in it all (see Matthew 1:20; Matthew 4:11; Matthew 28:2; Luke 1:26; Luke 2:9; Luke 22:43; John 1:51), — angels, of whom He ‘was seen’ (1Timothy 3:16) ,— covet now to exchange places with you that they may gaze into the mystery.”  The word which has here shrunk into our word “to look into,” means really, to bend aside to see. In its literal sense it occurs in John 20:5; John 20:11, and in Luke 24:12 (a verse not found in the best text), of people standing at the side of the cave so as not to get in their own light, and stooping sideways to peer in.  Metaphorically it is used in James 1:25.  It seems to mean a strained attention to something which has caught your eye somewhat out of your usual line of sight. Here then, the intention is to show that we are in a better position to understand the mysteries of redemption, not only than prophets, but also than angels; and they covet to stoop from their own point of view to ours.  And why so?  Not because of the inherent mysteriousness of the union of the two natures in Christ, for of that they are as intelligent as we, or more so; but because they are incapable of fully understanding human nature, flesh and blood, with its temptations and pains, its need of a Saviour. Charles Wesley well strikes the meaning in many of his poems: as —
“Ask the Father’s Wisdom how, Him that did the means ordain; Angels round our altars bow to search it out in vain;”
“Angels in fixt amazement around our altars hover, with eager gaze adore the grace of our Eternal Lover.”
Though very possibly the divine intention of the cherubim over the mercy-seat (Exodus 25:20) may have been to symbolise that which is here said, yet it is not to be thought that St. Peter was consciously thinking of the symbol.

Benson Commentary : To obtain a more perfect insight into, and knowledge of, as being matters of their admiration and delight, because in them the manifold wisdom of God is displayed, and by them the salvation of men is procured and effected, which they rejoice in.  The expression, the angels desire to look into, is literally, to stoop down to. “But stooping being the action of one who desires to look narrowly into a thing, it properly means to look attentively.  The omission of the article before αγγελοι, angels, renders the meaning more grand. Not any particular species of angels, but all the different orders of them, desire to look into the things foretold by the prophets, and preached by the apostles.  See Ephesians 3:10.  This earnest desire of the angels to contemplate the sufferings of Christ, was emblematically signified by the cherubim placed in the inward tabernacle, with their faces turned down toward the mercy-seat, Exodus 25:20.  To that emblem there is a plain allusion in the word παρακυψαι here, to stoop.  The apostle’s meaning is, If our salvation, and the means by which it is accomplished, are of such importance as to merit the attention of angels, how much more do they merit our attention, who are so much interested in them!” — Macknight.
Here is a beautiful gradation: prophets, righteous men, kings, desired to hear and see the things which Christ did and taught, Matthew 13:17; but what the Holy Ghost taught concerning Christ, the very angels long to understand.

Jamieson-Fausset Commentary : Angels—still higher than “the prophets” (1 Peter 1:10). Angels do not any more than ourselves possess an INTUITIVE knowledge of redemption. “To look into” in Greek is literally, “to bend over so as to look deeply into and see to the bottom of a thing.”  See on [2612] James 1:25, on same word.  As the cherubim stood bending over the mercy seat, the emblem of redemption, in the holiest place, so the angels intently gaze upon and desire to fathom the depths of “the great mystery of godliness, God manifest in the flesh, justified in the Spirit, seen of angels” (1 Timothy 3:16).  Their “ministry to the heirs of salvation” naturally disposes them to wish to penetrate this mystery as reflecting such glory on the love, justice, wisdom, and power of their and our God and Lord.  They can know it only through its manifestation in the Church, as they personally have not the direct share in it that we have. “Angels have only the contrast between good and evil, without the power of conversion from sin to righteousness: witnessing such conversion in the Church, they long to penetrate the knowledge of the means whereby it is brought about”

Meyer’s NT : properly, “to bend to the side so as to examine a thing,” means when joined with ΕἸς not only: “to look towards,” but: “to look into anything,” and that in order to obtain a more accurate knowledge of the object in question.[78] The παρά of the verb indicates that the angels stand outside the work of redemption, inasmuch as it is not for them, but for man (cf. Hebrews 2:16).  The addition of this clause brings prominently forward the idea, not that the work of salvation is a mystery,  — concealed even from the angels, — but that that which has been proclaimed to the readers is something so glorious that even the angels had a wish and a longing to see what was its fashion, and what the course of its development (cf. Ephesians 3:10)