Let $V$ be a finite-dimensional vector space over some field $K$, $V^*$ be its dual and $\mathcal{T}(V)$ be its tensor algebra. If $K$ is either $\mathbb{R}$ or $\mathbb{C}$, then every multilinear form
$$V\times\cdots\times V \times V^*\times\cdots\times V^* \longrightarrow K$$
can be canonically identified with one element of $\mathcal{T}(V)$ (and one element only).
If we consider $K=\mathbb{C}$, though, no element of $\mathcal{T}(V)$ can be identified with an antilinear operator, sesquilinear form or any application that's antilinear with respect to some variables (and linear for the rest of them), right?
If so, can the tensor algebra of $V$ be extended so that it also contains tensors canonically identifiable with those?, how?