Let $F$ and $E$ be two subfields of a fixed field $K$, then the compositum $F.E$ is just $F(E)=E(F)$.
Let $K_2$ be the second Milnor algebraic K-group.
I ma asking if we can express (or lift ) elements of $K_2(F.E)$ in terms of those in $K_2(F)$ and $K_2(E)$?
If not in general. Are there specific cases for which this holds?