Servicemember Retirement Improvement Act This bill allows members of the Ready Reserve of a reserve component of the Armed Forces to make the maximum allowable contribution ($19,500 in 2020) to their Thrift Savings Plans (TSPs) without limiting the amount such members may contribute to a retirement plan based upon other employment. The bill also doubles the maximum allowable contribution amount to the TSPs of federal employees in the Ready Reserve who are not eligible to make contributions to any plan other than the TSP.