[This is quite an extensive subject and I do not wish to have to append all the relevant texts. I am assuming that anyone interested will reference a concordance and look up all that is necessary. To fully document all of this would be unreasonable, so I offer it in its present form.]
Hebrew references are as found in Young's Analytical Concordance.
Kethoneth [Strong 3801, 'kethoneth or kuttoneth']
Kethoneth, garment, is mentioned seven times - a perfect number - in Genesis: once in relation to the coats of skins which God provided for Adam and Eve, then six times regarding Joseph’s garment. Joseph’s garment appears after his death, with blood upon it - a significant matter.
Joseph’s garment is that which sets him apart from his brethren - also a significant matter.
Then kethoneth appears seven times in Exodus relating to Aaron and his sons. It is a matter of priestly attire and priestly service. Only the God-appointed High Priest and his sons may don this attire.
Kethoneth appears twenty seven times in scripture (the quoted number, in one concordance, of "twenty nine" is incorrect). Twenty seven is a highly significant number and draws very great attention to this matter. Three times three times three is extremely significant.
Passim [Strong 6446 pas/passim ]
Passim - a plural Hebrew word - is what is behind the English ‘many colours’. It occurs five times in scripture, five being a matter of pilgrimage, see Benjamin and portions. Three times it relates to Joseph’s garment and twice to Tamar’s. II Samuel 13: 18,19 makes clear that the coat is a matter of King’s daughters and virginity.
BDB seems to indicate that the word used in clothing context means a 'tunic reaching to palms and soles', which I take it means merely a cloak that covers the whole of the exposed parts of the body. It may be that colour is nothing to do with the subject.
One set apart, as Joseph; then, King’s daughters and virginity, as Tamar.
Pas, a Chaldee word, means ‘a part‘. Thus the plural, passim, is a matter of diversity of parts. The part, pas, in question is a matter, Daniel 5: 5, 24, of the hand of judgement coming forth.
Thus the coat is a matter of One who takes upon him diversity.
And that diversity relates to judgment.
And this sets him apart from his brethren.
But he does it for his brethren and his brethren’s benefit.
He takes not this privilege himself.
He is appointed to it by the father.
His father will suffer grief for this.
There will be death - and bloodshed.
The son will be distanced from the father.
My God, My God, why hast thou forsaken me ?
As with many examples of prophetic imagery, there is a mixture of allusion. It is as though a reflection upon water breaks, re-forms, coalesces and forms again. One sees more than one thing in the imagery.
So with Joseph. He is set forth both as Christ and also as Christ’s pilgrim people.