For commutative algebras there are three important homology theories, Harrison homology, Andr\'e-Quillen homology and Gamma-homology. In general these differ, unless one works with respect to a ground field of characteristic zero.
I will explain why the analogues of these homology theories agree in the category of pointed commutative monoids in symmetric sequences, aka pointed commutative shuffle algebras and I'll give examples of such algebras.
In addition, there is a natural model category structure on the category of pointed dg commutative shuffle algebras and this is Quillen equivalent to the model category of pointed simplicial commutative shuffle algebras.