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We use computational high-throughput techniques to study the thermodynamic stability of ternary type I Si clathrates. Two strategies to stabilize the structures are investigated: through endohedral doping of the 2a and 6d Wyckoff positions (located at the center of the small and large cages, respectively) and by substituting the Si 6c positions. Our results agree with the overwhelming majority of experimental results and predict a series of unknown clathrate phases. Many of the stable phases can be explained by the simple Zintl–Klemm rule, but some are unexpected. We then successfully synthesize one of the latter compounds, a new type I silicon clathrate containing Ba (inside the cages) and Be (in the 6c position). These results prove the predictive power and reliability of our strategy and motivate the use of high-throughput screening of materials properties for the accelerated discovery of new clathrate phases.