Group self‐annuitization (GSA) schemes are designed to share uncertain future mortality experience including systematic improvements. Challenges for designing group pooled schemes include decreasing average payments when mortality improves significantly, decreasing numbers in the pool at older ages, and the impact of dependence from systematic mortality improvements across different ages of members in the pool. This article uses a multiple‐factor stochastic mortality model in a simulation study to show how pooling can be made more effective and to quantify the limitations of these pooling schemes arising from the impact of systematic longevity risk.