The Bible directs us to invoke those in heaven and ask them to pray with us.
Thus, in Psalm 103 we pray
"Bless the Lord, O you his angels, you mighty ones who do his word, hearkening to the voice of his word! Bless the Lord, all his hosts, his ministers that do his will!" (Ps. 103:2021).
And in the opening verses of Psalms 148 we pray
"Praise the Lord! Praise the Lord from the heavens, praise him in the heights! Praise him, all his angels, praise him, all his host!"
Not only do those in heaven pray with us, they also pray for us. In the book of Revelation, John sees that "the twenty-four elders [the leaders of the people of God in heaven] fell down before the Lamb, each holding a harp, and with golden bowls full of incense, which are the prayers of the saints" (Rev. 5:8). Thus the saints in heaven offer to God the prayers of the saints on earth.
Angels do the same thing:
"[An] angel came and stood at the altar [in heaven] with a golden censer; and he was given much incense to mingle with the prayers of all the saints upon the golden altar before the throne; and the smoke of the incense rose with the prayers of the saints from the hand of the angel before God" (Rev. 8:34).
Jesus himself warned us not to offend small children, because their guardian angels have guaranteed intercessory access to the Father:
"See that you do not despise one of these little ones; for I tell you that in heaven their angels always see the face of my Father who is in heaven" (Matt. 18:10).
Because he is the only God-man and the Mediator of the New Covenant, Jesus is the only mediator between man and God (1 Tim. 2:5), but this in no way means we cannot or should not ask our fellow Christians to pray with us and for us (1 Tim. 2:14). In particular, we should ask the intercession of those Christians in heaven, who have already had their sanctification completed, for "[t]he prayer of a righteous man has great power in its effects" (Jas. 5:16).
The word "pray" means "to make a request"; although this meaning is obsolete in current American English, it was a common and standard usage well into the middle of the 19th Century. There are many, many examples in the bible of people praying to someone other than God. Here are a few examples from the book of Genesis:
Say, I pray thee, thou art my sister: that it may be well with me for thy sake; and my soul shall live because of thee" Gen 12:13
And Abram said unto Lot, Let there be no strife, I pray thee, between me and thee, and between my herdmen and thy herdmen; for we be brethren. Is not the whole land before thee? separate thyself, I pray thee, from me: if thou wilt take the left hand, then I will go to the right; or if thou depart to the right hand, then I will go to the left." Gen 13:8-9
And Sarai said unto Abram, Behold now, the LORD hath restrained me from bearing: I pray thee, go in unto my maid; it may be that I may obtain children by her. And Abram hearkened to the voice of Sarai. Gen 16:2
And said, My Lord, if now I have found favour in thy sight, pass not away, I pray thee, from thy servant: Let a little water, I pray you, be fetched, and wash your feet, and rest yourselves under the tree: Gen 18:3-4
And he said, Behold now, my lords, turn in, I pray you, into your servant's house, and tarry all night, and wash your feet, and ye shall rise up early, and go on your ways. And they said, Nay; but we will abide in the street all night. Gen 19:2
And said, I pray you, brethren, do not so wickedly. Behold now, I have two daughters which have not known man; let me, I pray you, bring them out unto you, and do ye to them as is good in your eyes: only unto these men do nothing; for therefore came they under the shadow of my roof. Gen 19:7-8
"Pray, sir, listen to me! I give you both the field and the cave in it; in the presence of my kinsmen I make this gift. Bury your dead!" Gen 23:11
And he spake unto Ephron in the audience of the people of the land, saying, But if thou wilt give it, I pray thee, hear me: I will give thee money for the field; take it of me, and I will bury my dead there. Gen 23:13
And Abraham said unto his eldest servant of his house, that ruled over all that he had, Put, I pray thee, thy hand under my thigh: Gen 24:2
And the servant ran to meet her, and said, Let me, I pray thee, drink a little water of thy pitcher." Gen 24:17
And from the New Testament
If only you would put up with a little foolishness from me! Pray put up with me. 2 Cor 11:1
With all prayer and supplication, pray at every opportunity in the Spirit. To that end, be watchful with all perseverance and supplication for all the holy ones and also for me, that speech may be given me to open my mouth, to make known with boldness the mystery of the gospel. Eph 6:18-19
Yes, and I pray thee also, my true yokemate, 3 to help them... Phillipians 4:3
Brothers, pray for us . 1 Thess 5:25
"First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all men, for kings and all who are in high positions, that we may lead a quiet and peaceable life, godly and respectful in every way. This is good, and pleasing to God our Savior, who desires all men to be saved and to come to the knowledge of the truth" (1 Tim. 2:14)
Praying for each other is simply part of what Christians do. Intercessory prayers offered by Christians on behalf of others is something "good and pleasing to God," not something infringing on Christs role as mediator.
And this was the understanding from the days of the earliest Christians:
Hermas
"[The Shepherd said:] But those who are weak and slothful in prayer, hesitate to ask anything from the Lord; but the Lord is full of compassion, and gives without fail to all who ask him. But you, [Hermas,] having been strengthened by the holy angel [you saw], and having obtained from him such intercession, and not being slothful, why do not you ask of the Lord understanding, and receive it from him?" (The Shepherd 3:5:4 [A.D. 80]).
Clement of Alexandria
"In this way is he [the true Christian] always pure for prayer. He also prays in the society of angels, as being already of angelic rank, and he is never out of their holy keeping; and though he pray alone, he has the choir of the saints standing with him [in prayer]" (Miscellanies 7:12 [A.D. 208]).
Origen
"But not the high priest [Christ] alone prays for those who pray sincerely, but also the angels . . . as also the souls of the saints who have already fallen asleep" (Prayer 11 [A.D. 233]).
Cyprian of Carthage
"Let us remember one another in concord and unanimity. Let us on both sides [of death] always pray for one another. Let us relieve burdens and afflictions by mutual love, that if one of us, by the swiftness of divine condescension, shall go hence first, our love may continue in the presence of the Lord, and our prayers for our brethren and sisters not cease in the presence of the Fathers mercy" (Letters 56[60]:5 [A.D. 253]).
Anonymous
"Atticus, sleep in peace, secure in your safety, and pray anxiously for our sins" (funerary inscription near St. Sabinas in Rome [A.D. 300]).
"Pray for your parents, Matronata Matrona. She lived one year, fifty-two days" (ibid.).
"Mother of God, [listen to] my petitions; do not disregard us in adversity, but rescue us from danger" (Rylands Papyrus 3 [A.D. 350]).
Methodius
"Hail to you for ever, Virgin Mother of God, our unceasing joy, for to you do I turn again. You are the beginning of our feast; you are its middle and end; the pearl of great price that belongs to the kingdom; the fat of every victim, the living altar of the Bread of Life [Jesus]. Hail, you treasure of the love of God. Hail, you fount of the Sons love for man. . . . You gleamed, sweet gift-bestowing Mother, with the light of the sun; you gleamed with the insupportable fires of a most fervent charity, bringing forth in the end that which was conceived of you . . . making manifest the mystery hidden and unspeakable, the invisible Son of the Fatherthe Prince of Peace, who in a marvelous manner showed himself as less than all littleness" (Oration on Simeon and Anna 14 [A.D. 305]).
"Therefore, we pray [ask] you, the most excellent among women, who glories in the confidence of your maternal honors, that you would unceasingly keep us in remembrance. O holy Mother of God, remember us, I say, who make our boast in you, and who in august hymns celebrate the memory, which will ever live, and never fade away" (ibid.).
"And you also, O honored and venerable Simeon, you earliest host of our holy religion, and teacher of the resurrection of the faithful, do be our patron and advocate with that Savior God, whom you were deemed worthy to receive into your arms. We, together with you, sing our praises to Christ, who has the power of life and death, saying, You are the true Light, proceeding from the true Light; the true God, begotten of the true God" (ibid.).
Cyril of Jerusalem
"Then [during the Eucharistic prayer] we make mention also of those who have already fallen asleep: first, the patriarchs, prophets, apostles, and martyrs, that through their prayers and supplications God would receive our petition . . . " (Catechetical Lectures 23:9 [A.D. 350]).
Hilary of Poitiers
"To those who wish to stand [in Gods grace], neither the guardianship of saints nor the defenses of angels are wanting" (Commentary on the Psalms 124:5:6 [A.D. 365]).
Ephraim the Syrian
"You victorious martyrs who endured torments gladly for the sake of the God and Savior, you who have boldness of speech toward the Lord himself, you saints, intercede for us who are timid and sinful men, full of sloth, that the grace of Christ may come upon us, and enlighten the hearts of all of us so that we may love him" (Commentary on Mark [A.D. 370]).
"Remember me, you heirs of God, you brethren of Christ; supplicate the Savior earnestly for me, that I may be freed through Christ from him that fights against me day by day" (The Fear at the End of Life [A.D. 370]).
The Liturgy of St. Basil
"By the command of your only-begotten Son we communicate with the memory of your saints . . . by whose prayers and supplications have mercy upon us all, and deliver us for the sake of your holy name" (Liturgy of St. Basil [A.D. 373]).
Pectorius
"Aschandius, my father, dearly beloved of my heart, with my sweet mother and my brethren, remember your Pectorius in the peace of the Fish [Christ]" (Epitaph of Pectorius [A.D. 375]).
Gregory of Nazianz
"May you [Cyprian] look down from above propitiously upon us, and guide our word and life; and shepherd this sacred flock . . . gladden the Holy Trinity, before which you stand" (Orations 17[24] [A.D. 380]).
"Yes, I am well assured that [my fathers] intercession is of more avail now than was his instruction in former days, since he is closer to God, now that he has shaken off his bodily fetters, and freed his mind from the clay that obscured it, and holds conversation naked with the nakedness of the prime and purest mind . . . " (ibid., 18:4).
Gregory of Nyssa
"[Ephraim], you who are standing at the divine altar [in heaven] . . . bear us all in remembrance, petitioning for us the remission of sins, and the fruition of an everlasting kingdom" (Sermon on Ephraim the Syrian [A.D. 380]).
John Chrysostom
"He that wears the purple [i.e., a royal man] . . . stands begging of the saints to be his patrons with God, and he that wears a diadem begs the tentmaker [Paul] and the fisherman [Peter] as patrons, even though they be dead" (Homilies on Second Corinthians 26 [A.D. 392]).
"When you perceive that God is chastening you, fly not to his enemies . . . but to his friends, the martyrs, the saints, and those who were pleasing to him, and who have great power [in God]" (Orations 8:6 [A.D. 396]).
Ambrose of Milan
"May Peter, who wept so efficaciously for himself, weep for us and turn towards us Christs benign countenance" (The Six Days Work 5:25:90 [A.D. 393]).
Jerome
"You say in your book that while we live we are able to pray for each other, but afterwards when we have died, the prayer of no person for another can be heard. . . . But if the apostles and martyrs while still in the body can pray for others, at a time when they ought still be solicitous about themselves, how much more will they do so after their crowns, victories, and triumphs?" (Against Vigilantius 6 [A.D. 406]).
Augustine
"A Christian people celebrates together in religious solemnity the memorials of the martyrs, both to encourage their being imitated and so that it can share in their merits and be aided by their prayers" (Against Faustus the Manichean [A.D. 400]).
"There is an ecclesiastical discipline, as the faithful know, when the names of the martyrs are read aloud in that place at the altar of God, where prayer is not offered for them. Prayer, however, is offered for the dead who are remembered. For it is wrong to pray for a martyr, to whose prayers we ought ourselves be commended" (Sermons 159:1 [A.D. 411]).
"At the Lords table we do not commemorate martyrs in the same way that we do others who rest in peace so as to pray for them, but rather that they may pray for us that we may follow in their footsteps" (Homilies on John 84 [A.D. 416]).
"Neither are the souls of the pious dead separated from the Church which even now is the kingdom of Christ. Otherwise there would be no remembrance of them at the altar of God in the communication of the Body of Christ" (The City of God 20:9:2 [A.D. 419]).
So since we are told to pray for each other, since the Apostles prayed people to pray for them, since we are united in Christ with our departed brethren in heaven who are not dead but are alive in the presence of God, since nowhere does the Bible say that we are to stop asking our brethren to pray for us merely because they are with God, and since Christians have been doing it since the days of the Apostles.... what makes you think that we are not allowed to ask them for their intercession? And whatever your reason is, what makes you think that I should look on you as an authority to whom I should listen?