The Barratt-Eccles operad is an operad in simplicial sets that provides a particularly nice model for the E_∞-operad; algebras in spaces over the Barratt-Eccles operad model E_∞-spaces, i.e., homotopy coherent commutative monoids in spaces. It can be described concretely by applying the nerve functor componentwise to an operad in groupoids, which itself is obtained by applying the codiscrete groupoid functor componentwise to an operad Σ in sets such that Σ(n) is the symmetric group of order n and the operadic composition Σ(n)×(Σ(a₁)×⋯×Σ(aₙ))→Σ(a₁+⋯+aₙ) is given by stacking the permutations in Σ(aᵢ) together and composing them with the block permutation in Σ(a₁+⋯+aₙ) induced by the permutation in Σ(n). Here the codiscrete groupoid functor sends a set X to the groupoid with X as the set of objects and exactly one morphism between any pair of objects; it is the right adjoint to the forgetful functor from groupoids to sets that sends a groupoid to its underlying set of objects.

I am interested in similarly spirited constructions for various cousins of E_∞-spaces.

Specifically, I am interested in the group-like E_∞-spaces, which can be thought of as homotopy coherent commutative groups and are a model for connective spectra.

Another interesting case is E_∞-ring spaces, which can be thought of as homotopy coherent commutative rings, and are a model for connective E_∞-ring spectra.

As pointed out by Peter May in his answer, operads cannot model such structures because they do not allow one to talk about operations with multiple outputs, so a part of the question is whether it is possible to express the above notions using some generalization of operads, e.g., properads, props, etc.

Is there an analog of the Barratt-Eccles construction for E_∞-groups and E_∞-rings?