Before revision:  Our results include a polynomial time approximation scheme for modular maximization with a constant number of multiple knapsack constraints and a matroid constraint, thus generalizing the best known results for the classic multiple knapsack problem as well as d-dimensional knapsack, for any d \geq 2.
After revision:  Our results include a polynomial time approximation scheme for Multiple-Choice Multiple Knapsack, improving upon the best known results for the classic multiple knapsack problem as well as d-dimensional knapsack, for any d \geq 2.