Artin's solution to Hilbert's seventeenth problem tells us that a multivariate polynomial $f$ takes only non-negative values over the reals if and only if it is a sum of squares of rational functions.

Now suppose that, in addition to taking only non-negative values over the reals, $f$ is a symmetric polynomial; i.e., it is invariant under any permutation of the variables. Is there anything more we can say about $f$ beyond the fact that it is a sum of squares of rational functions? For example, can we say anything about what $f$ looks like when expanded in terms of various well-known bases for symmetric functions?