Man of the West is quite right!
I was told that during the minor elevation, one should ask for special requests; has anyone else heard this? Is this accurate?
I have never heard of this before. However, from the Consecration to the distribution of Holy Communion you have the Author of grace Himself there upon the Altar, and all the while you can ask Him with filial confidence, humility, and reverent joy anything you wish (provided it is according to His will, and suited to your state of life or the state of life for whom you are praying).
The Minor Elevation occurs at the great doxology that ends the sacred Canon,
Per ipsum, et cuм ipso, et in ipso, est tibi Deo Patri omnipotenti, in unitate Spiritus Sancti, omnis honor et gloria, "Through Him, and with Him, and in Him, is all honor and glory unto Thee, God the Father almighty, in the unity of the Holy Ghost."
If one reflects well upon the text of this doxology, the Priest is offering unto the heavenly Father the bloodless re-presentation of the sacrifice of His only-begotten Son, co-equal and co-substantial unto Him from all eternity, which the Priest has just confected moments before upon the sacred Altar by the Mystery of Transubstantiation.
It is becoming for one, at this very solemn oblation of the sacrifice of the Word Incarnate, to offer up prayers of petition, together with acts of charity, praise, thanksgiving, etc.
I personally make acts of praise and self-abasement whilst the Priest pronounces these words, because the Lord's Prayer shall forthwith follow, the most beautiful thing that created effability could ever make, since it was composed and pronounced by our Divine Savior for our own sakes. In the
Pater noster is to be found all petitions one can possibly make. But that's just my personal take on it.