The Multiple-Choice Multi-Dimensional knapsack (MMKP) problem is defined as follows. The input is $N$ groups of items, each item in each group has a value, and requires $m$ resources. The total available resources is given by a vector $R = (r_1, r_2, .., r_m) $. The goal is to choose exactly one item from each group, such the the total value is maximized and the resource constraints hold.
If we would add to the problem the constraint that each item requires at most $n \ll m$ of the resources, will the new problem remain as hard as the original MMKP?