In the benders decomposition, is it possible to decompose the master problem as follows and let the subproblem become the subproblem of the new subproblem? Let's say that we have the following problem.
$y$ is a binary variable, $x$ and $z$ are continuous and take values between $0$ and $1$.
$$\max_{x∈X, y∈Y}(cx - \min_{z∈Z(y)}dxz)$$
Is it possible to decompose it further, as follows?
\begin{align}\text{Master Problem:}&\quad\max_{y∈Y} θ\\\text{Subproblem 1}&\quad\max_{x∈X(y)} cx\\\text{Subproblem 2}&\quad\min_{z∈Z(y)} d\bar xz\end{align}
Subproblem 1 contains constraints that include $y$.
Subproblem 2 contains constraints that include $y$.
If yes, is there any sources to look up while developing the algorithm and constraints correctly to solve this problem? If not, what are the best ways to solve a large-scale master problem?
Edit: There was maximization in subproblem 2 by mistake, changed it to minimization. Edited the notation.