We describe a new class of mechanisms—referred to as booster draft mechanisms—for allocating $$n\times m$$ indivisible objects among n individuals with responsive preferences . Specifically, n individuals are assigned m objects each, from m different sets of size n —called boosters—and simply receive their highest ranked object, among the remaining objects in each booster, when it is their turn to choose. We contrast booster draft mechanisms with two well-known alternatives: serial dictatorship and draft mechanisms. Our results suggest that booster draft mechanisms pose a viable alternative for resolving multi-object assignment problems.