From the answers to this question it seems that most if not all Jewish sources treat Trinitarian Christianity (in particular, their doctrine of the Trinity) as either Shittuf or outright Avoda Zara, both of which (if there is a difference) are expressly forbidden for Jews to believe.
For background, the Christian doctrine of the Trinity explains the Godhead as: "the Father is God, the Son is God, and the Holy Spirit is God, and yet there are not three Gods but one God" (in the Athanasian Creed) and therefore Christians would seem to be monotheists, except that God has parts or aspects which cannot be understood but together comprise God's unity (since the Trinity is classified as a 'mystery'). It is this doctrine which is problematic in Jewish sources (which were, of course, not written by Christian theologians but Jewish ones whose understanding of Christian doctrine was probably similar to the level I just presented).
In the Jewish Kabbalistic doctrine of Sefirot, there are 10 Sefirot which are often described as either parts of God's "body" (each corresponding to a different limb) or manifestations or emanations, which although separate, with unique properties and sometimes male or female associations, nevertheless somehow do not contradict that God remains unified and indivisible. His unity is also, in this sense somewhat mysterious.
The Rivash (Rabbi Isaac Ben Sheshet, 14th Century) famously wrote in a responsum, #157:
.וכל זה הוא דבר זר מאוד בעיני מי שאינו מקובל כמו הם; וחושבים, שזה אמונת שניות. וכבר שמעתי אחד מן המתפלספים מספר בגנות המקובלים, והיה אומר: הנוצרים מאמיני השילוש, והמקובלים מאמיני העשיריות
And all this is very foreign in my eyes, as someone who is not a Kabbalist such as myself; and they think is is dualist theology...and I heard one of the ones who philosophizes speaking to the detraction of the Kabbalists, saying: the Christians believe in 3 and the Kabbalists believe in 10.
If the Christian doctrine of the Trinity as understood by Jews is deemed Shittuf/Avoda Zara by them, is the Kabbalistic doctrine of Sefirot considered that as well?
Is there any reason to distinguish between the Christian divided/united God as understood by Jews (and deemed by them problematic) and the Kabbalistic one?
(Note that I am not interested in whether the doctrine of incarnation is problematic from a Jewish perspective. I would like to explore merely the question of a multipart Godhead and whether there is any reason to distinguish Christian and Jewish beliefs in that regard alone. Is there some difference in the perspective on the "parts"? Or a difference in the interpretation of the level of independence of the "parts"? Or a difference in regards their unification/unity? Or is there not fundamental difference aside from incarnation?)