In this paper we examine the impact of using the Sherali-Adams procedure on highly symmetric integer programming problems. Linear relaxations of the extended formulations generated by Sherali-Adams can be very large, containing on the order of n choose d many variables for the level-d closure. When large amounts of symmetry are present in the problem instance however, the symmetry can be used to generate a much smaller linear program that has an identical objective value. We demonstrate this by computing the bound associated with the level 1, 2, and 3 relaxations of several highly symmetric binary integer programming problems. We also present a class of constraints, called counting constraints, that further improves the bound, and in some cases provides a tight formulation.