There is an analogous to the inerpolation theorem of Aronszajn-Gagliardo for multilinear operators in Banach spaces?

Question

The Aronszajn-Gagliardo theorem states that on the category $\mathcal B$ of Banach spaces, given $A$ an interpolation space with respect to the couple $\overline A$ there exists an exact interpolation functor $F$ on $\mathcal B$ such that $F(\overline A)=A$.

i.e. If $T:\overline A\to\overline B$ then $T:F(\overline A)\to F(\overline B)$ with $\|T\|_{F(\overline A),F(\overline B)}\leq\max\{\|T\|_{A_0,B_0},\|T\|_{A_1,B_1}\}$.

There is an analogous result in the context of multilinear operators on Banach spaces?