This paper investigates the potential benefits resulting from using two different types of friction dampers on a bladed disk. In this scenario, every blade or platform is equipped with a damper of either type A or type B with these two types differing by their friction forces. The variations in friction force are assumed here to be induced by similar variations in the damper mass. The benefit of this strategy is measured in comparison with using identical dampers of optimized mass on every blade/platform and is dependent on the pattern of A/B dampers around the disk as well as the damper masses. It is accordingly desired to optimize both the pattern and the damper masses to obtain the largest benefit. As a discovery effort, this optimization is accomplished here through an exhaustive search for all patterns and on a large grid of values of the two damper masses. Owing to the large computational cost of this effort, only single degree of freedom per blade models are assumed with both blade-blade and blade-ground dampers and only small blade counts are considered (6 and 12). Three particular situations are considered: disks with tuned blades except for the arrangement of A/B dampers, disks that also exhibit random mistuning of the blade stiffnesses, and, finally, disks exhibiting random mistuning of both blade stiffness and of the friction forces of the dampers. This latter situation is considered to include the variability induced by manufacturing and wear on the friction dampers. In all cases considered, the benefit of this intentional mistuning of friction dampers is either zero or small, of the order of a few percent, consistently with a single data point reported in the literature.