What is a basis for the space of multilinear maps from $V_1 \times \dots \times V_k \to W$?

Question

I know that a basis for the space $L(V_1, \dots, V_k; \mathbb R)$ is $$\{\varepsilon^{i_1} \otimes \cdots \otimes \varepsilon^{i_k}\mid 1 \le \varepsilon^{i_j} \le \dim(V_j)\}$$ where $\varepsilon^{i_j}$ is the dual basis vector to the basis vector $E_{i_j}$ for $V_j$.

But what if we change this to $L(V_1, \dots, V_k; W)$. What would be a basis for this space?