This paper presents a novel private presence protocol, referred to as MP3, where the service provider does not have any knowledge of the social graph of its users. In prior work, a private presence protocol, referred to as DP5, was presented. However, the size of the presence database in this protocol grows rapidly as the number of users increases; this limits its scalability and increases its cost. In the proposed protocol, the size of the presence database is reduced significantly, enabling significantly cheaper registration and lookup compared to that of DP5. MP3 requires about two-thirds the bandwidth of DP5 for N = 200 000 users and about one-half the bandwidth of DP5 for N = 1 000 000 users. Furthermore, these savings grow asymptotically with the number of users. Additionally, the client-facing latency in MP3 is an order of magnitude less than that of DP5. We provide an evaluation of the performance and scalability of both protocols.