multivariable calculus – Is there a way to better write chains of multivariate functions?

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?