In a single variable, if $f, g, h$ are functions with compatible domains and codomains, we use the notation $f \circ g \circ h$ to have a more readable version of $f(g(h(x)))$.
Now consider for example the function $S(X,Y,Z)$ where $X(u,v), Y(u,v), Z(u,v)$ are functions of 2 variables and $u,v$ are functions of the variable $t$. Writing the full composition of $S$ in terms of $t$ would involve a lot of parenthesis and is kinda hard to read.
Is there a similar notation convention to chain multivariate functions as there is for univariate ones?
A shorter notation I have seen is $S(X(\vec x),Y(\vec x),Z(\vec x))$. If you don't want to name the variables, there's also $S(X(-),Y(-),Z(-))$ (or replace $-$ with $\cdot$), even though I don't know if that would be good enough.
It feels (to me) that $S\circ(X,Y,Z)$ should be valid, but I have not seen many such usages.