Secret Sharing (SS) is widely adopted in secure Multi-Party Computation (MPC) with its simplicity and computational efficiency. However, SS-based MPC protocol introduces significant communication overhead due to interactive operations on secret sharings over the network. For instance, training a neural network model with SS-based MPC may incur tens of thousands of communication rounds among parties, making it extremely hard for real-world deployment.To reduce the communication overhead of SS, prior works statically convert interactive operations to equivalent non-interactive operations with extra computation cost. However, we show that such static conversion misses chances for optimization, and further present SOLAR, an SS-based MPC framework that aims to reduce the communication overhead through dynamic communication-computation conversion. At its heart, SOLAR converts interactive operations that involve communication among parties to equivalent non-interactive operations within each party with extra computations and introduces a speculative strategy to perform opportunistic conversion when CPU is idle for network transmission. We have implemented and evaluated SOLAR on several popular MPC applications, and achieved 1.6-8.1 times speedup in multi-thread setting compared to the basic SS and 1.2-8.6 times speedup over static conversion.