Within the concept of gilgulim there is a distinction between reincarnation into any body that may be ready for his gilgul, and reincarnation through a brother, which is the sod [meaning "secret"] of yibum.
Yibum is the Levirate marriage in which a surviving brother marries his (widowed) sister-in-law whose husband, the man's brother, has died childless.
In a normal gilgul, the Nefesh, Ruach and Neshama [NR"N] do not reincarnate together, or even two at once. Only the Nefesh reincarnates until it is rectified. Afterwards, in another gilgul, the Nefesh and Ruach return together until they are rectified. When that occurs, then the entire NR"N [reincarnates together] until the Neshama is rectified, which completes his gilgulim. Or, sometimes each of the three reincarnates individually [and achieves tikun independent of the others]: the Ruach with another Nefesh in another body, and the Neshama with a different Nefesh and Ruach in a different body.
However, when a man reincarnates through his brother, the entire NR"N may do so together.
Chaim Vital says: It seems from Sabba of Mishpatim that even with respect to yibum all three do not come back together, but only the Nefesh and the Ruach without the Neshama. This requires further investigation.
Thus, it is not clear if just the N"R come together in one gilgul during yibum, or if all three come together at one time. In either case, it is different than a regular gilgul.
End of Introduction [Chapter Two].
[Commentary by Shabtai Teicher.]