Data sharing between social impact organizations has the potential to amplify social impact by reducing redundant efforts and increasing capacity. Unfortunately, the risks of and restrictions on sharing personal data often limit this potential. New technologies such as secure multi-party computation (MPC) promise to mitigate many of these risks while retaining many of the benefits of traditional data-sharing solutions. In this paper we investigate the use of MPC to solve the record linkage problem of analyzing referral loops between service providers. Initial results indicate that the proposed MPC solution produces correct aggregate results compared to the status quo methods of manual and automatic analysis on plaintext.