We present a relational MPC framework for secure collaborative analytics on private data with no information leakage. Our work targets challenging use cases where data owners may not have private resources to participate in the computation, thus, they need to securely outsource the data analysis to untrusted third parties. We define a set of oblivious operators, explain the secure primitives they rely on, and analyze their costs in terms of operations and inter-party communication. We show how these operators can be composed to form end-to-end oblivious queries, and we introduce logical and physical optimizations that dramatically reduce the space and communication requirements during query execution, in some cases from quadratic to linear or from linear to logarithmic with respect to the cardinality of the input. We implement our framework on top of replicated secret sharing in a system called Secrecy and evaluate it using real queries from several MPC application areas. Our experiments demonstrate that the proposed optimizations can result in over 1000x lower execution times compared to baseline approaches, enabling Secrecy to outperform state-of-the-art frameworks and compute MPC queries on millions of input rows with a single thread per party.