Let $Sp^{\Sigma}$ be the category of symmetric spectra, and let $Sp^{\Sigma}-alg$ be the associated category of augmented commutative algebras. These are simplicial categories.

A question for experts: Can anyone give me a reference for, or explain a construction of, a *simplicial* functor
$$ Sp^{\Sigma} \rightarrow Sp^{\Sigma}-alg$$
which looks like the functor $X \mapsto \Sigma^{\infty}_+ \Omega^{\infty}X$ in the homotopy category?

Nick Kuhn