We can naively consider an operad as a collection $\{P(n)\}_{n\geq 0}$ of vector spaces $P(n)$ consisting of "functions" with $n$ inputs and one output, equipped with a number of compositions $$P(m)\times P(n)\to P(m+n-1)$$ given by attaching the output of an element of $P(n)$ to one of the inputs of an element of $P(m)$.

A dioperad generalises this to allow multiple outputs. So we have a collection $\{P(n,m)\}$, and a composition $$P(n_1,m_1)\times P(n_2,m_2)\to P(n_1+n_2-1, m_1+m_2-1)$$ where we attach one output to one input.

My question is whether there is a similar structure in the literature where we allow ourselves to attach multiple inputs to multiple outputs? Some sort of poly-operad