Cyclic homology may be defined as the primitive part (with respect to a natural product) of the homology of the Lie algebra associated with the "stabilization" of an associative algebra $A$. Here the "stabilization" is the matrix algebra $Mat_n(A)$, where $n$ goes to infinity. This definition explains another name of cyclic homology - "additive K-theory".
I believe that there exists an analogous notion for $e_n$-algebras. For a $e_n$-algebra $A$ it must be the primitive part of the homology of the Lie algebra associated with a $e_n$-algebra, which is an appropriate "stabilization" of $A$.
Whether anyone has some ideas how this thing could be defined? What is the homology of the trivial algebra? Is it an additive version of something?