To be clear: certain doctrines, in fact, a great many that all 'Christians' believe, do not have their 'basis' or 'origin', strictly speaking, in the Bible. So much as the Bible approves, dissapproves, teaches and allows certain things. But it doesn't prescribe, necessarily, every doctrine which was formative in the Church and its faith: a great example being the canon of Scripture itself. Some of it is descriptive, not prescriptive of valid doctrines, offices etc.
A good example is a valid office of what we might call the 'Seat of Moses', similar to, and probably a shadow of 'the Chair of Peter'. Jesus explicitly confirms and recognizes this office of leadership as something pre-existing His own ministry, and which is valid: Matthew 23:1-3.
The Issue of Canon
Several passages prove this. Many proofs are in the books rejected by the Reformers, called by them the 'Apocrypha' (unscriptural books relegated to the back of their Bible, and subsquently completely out of their Bible altogether) but which were nonetheless at the least formative of religious practice in the earliest Church; their Bible being, for a great time, the Greek Septuagint, which includes the Alexandrian, 'longer' canon.
The 'Deuterocanon'ical proofs
2 Maccabees 12:40-46
And they found...the slain...And so betaking themselves to prayers, they besought him, that the sin which had been committed might be forgotten....And making a gathering, he sent twelve thousand drachmas of silver to Jerusalem for sacrifice to be offered for the sins of the dead, thinking well and religiously concerning the resurrection, (For if he had not hoped that they that were slain should rise again, it would have seemed superfluous and vain to pray for the dead), And because he considered that they who had fallen asleep with godliness, had great grace laid up for them. It is therefore a holy and wholesome thought to pray for the dead, that they may be loosed from sins.
- Prayer for the 'dead.'
- For the purpose of loosing them from their sins (the definition of Purgatory) cf. Hebrews 13:3; Matthew 5:25-16. This is the logic.
- This constitutes an effectual prayer between all the saints of God, living and 'dead'.
(I personally find a certain drawing upon this language and theme in James 5:15:)
And the prayer of faith shall save the sick [dying] man: and the Lord shall
raise him up [the context of resurrection]: and if he be in sins, they shall be forgiven him.
(Again, only what I personally see to be a possible paraphrastic-style reference: since Catholicism holds that the sacrament of Extreme Unction described in James 5 is for the sick in danger of death, and that the sacrament prepares them to enter into heavenly glory without Purgation)
2 Maccabees 15:12-14
Onias who had been high priest...holding up his hands, prayed for all the people of the Jews: After this there appeared also another man, admirable for age, and glory, and environed with great beauty and majesty: Then Onias answering, said: This is a lover of his brethren, and of the people of Israel: this is he that prayeth much for the people, and for all the holy city, Jeremiah the prophet of God.
Needless to say, Jeremiah was long 'dead'.
- Ongoing intercession of the quote-unquote 'dead' saints (here Jeremiah) for the people of God.
When thou didst pray...I offered thy prayer to the Lord. ... For I am the angel Raphael, one of the seven, who stand before the Lord.
- Angels can pray for us/bring our petitions/prayers to God
- Thus, they are clearly 'aware' of our prayers at the least
This has to be Scripture, for St. John tells us this is exactly what happens in heaven, even though the book of Tobit tells this divine truth centuries in advance:
And I saw seven angels standing in the presence of God; and there
were given to them seven trumpets. And another angel came, and stood
before the altar, having a golden censer; and there was given to him
much incense, that he should offer of the prayers of all saints
upon the golden altar, which is before the throne of God.
- Confirms Tobit and what it says about intercession/prayer: angels can and do pray for us/bring our petitions/prayers to God
Revelation 5:8, by saying the exact same of the 'elders,' human saints, asserts that both saints and angels can pray for us. This is what we would expect, since Jesus tells us men shall be like the angels and equal to them, sons of God (My 22:30; Lk 20:36).
SAINTS AND ANGELS, IN HEAVEN, OFFERING PRAYERS ON OUR BEHALF TO GOD
There was a certain rich man, who was clothed in purple and fine linen; and feasted sumptuously every day. And there was a certain beggar, named Lazarus, who lay at his gate... And it came to pass, that the beggar died, and was carried by the angels into Abraham's bosom. And the rich man also died: and he was buried [and was] in [the abode of the dead]. And lifting up his eyes when he was in torments, he saw Abraham afar off, and Lazarus in his bosom: And he cried, [prayer/pleading to a 'dead' saint] and said: Father Abraham, have mercy on me, and send Lazarus, that he may dip the tip of his finger in water, to cool my tongue: for I am tormented in this flame. And Abraham said to him: Son, remember that thou didst receive good things in thy lifetime, and likewise Lazareth evil things, but now he is comforted; and thou art tormented. And besides all this, between us and you, there is fixed a great chasm: so that they who would pass from hence to you, cannot, nor from thence come hither. And he said: Then, father, I beseech thee, that thou wouldst send him to my father's house, for I have five brethren, that he may testify unto them, lest they also come into this place of torments. And Abraham said to him: They have Moses and the prophets; let them hear them. But he said: No, father Abraham: but if one went to them from the dead, they will [change their ways]. And he said to him: If they hear not Moses and the prophets, neither will they believe, [even] if one [should] rise again from the dead.
(notesmine, for readability and some commentary as relevant to the question)
The most important part is that Jesus takes communication between the spirits of the dead for granted—as very much possible; their being able to be present with each other the only thing not possible.
Abraham is called 'father,' in a spiritual sense, disproving the novel idea that "call no man father" forbids, or means forbidding this.
There are arguments on both sides as to whether this better suits a description of Purgatory (the rich man) or the Hell of the damned, or the respective places for those destined therefore when the abode of the dead was simply Sheol.
- Abraham declines, and does not reject the idea of, sending Lazarus to inform the brothers of the rich man.
And when she hath found [the coins she had lost], call together her friends and neighbours, saying: Rejoice with me, because I have found the [silver coin] which I had lost. So I say to you, there shall be joy among the angels of God upon one sinner [who turns from sin].
I say to you, that even so there shall be joy in heaven upon one
sinner that [turns from sin] more than upon ninety-nine [righteous] who [are in no need of turning from sin].
- Angels and saints (verse 7) can witness repentence, and thus hear our prayers, too, as Revelation shows clearly.
Abel...Enoch...Noah...Abraham...Isaac...Jacob...Sarah...Joseph...Moses...Rahab...Gideon...Barak...Samson...Jephthah...David...Samuel...the prophets... ... [ie. all the saints of God] Therefore, since we are surrounded by such a great cloud of witnesses, let us throw off everything that hinders and the sin that so easily entangles. And let us run with perseverance the race marked out for us...
You have not come to a mountain that can be touched and that is burning with fire; to darkness, gloom and storm...But you have come to Mount Zion, to the city of the living God, the heavenly Jerusalem. You have come to...to the spirits of the righteous made perfect...
- All the saints, who are "the spirits of the rigteous made perfect" can witness us, and surroung us while we run the race of refraining from sin—running the race of salvation. The angels (and saints) would necessarily need to know what we are doing in order to minister to us: Hebrews 1:14; cf. Matthew 18:10. And to be able to cater to our needs in order to "minister" to us for our salvation: for which they obviously pray, as that is the only way to recieve grace from God to help someone else.