We present a progress report of our project aiming to increase the number of known Cepheids in double-lined binary (SB2) systems from six to 100 or more. This will allow us, among other goals, to accurately measure masses for a large sample of Cepheids. Currently, only six accurate Cepheid masses are available, which hinders our understanding of their physical properties and renders the Cepheid mass–luminosity relation poorly constrained. At the same time, Cepheids are widely used for essential measurements (e.g., extragalactic distances, the Hubble constant). To examine Cepheid period–luminosity relations, we selected as binary candidates Cepheids that are too bright for their periods. To date, we have confirmed 56 SB2 systems, including the detection of significant orbital motions of the components for 32. We identified systems with orbital periods up to five times shorter than the shortest reported period to date, as well as systems with mass ratios significantly different from unity (suggesting past merger events). Both features are essential to understand how multiplicity affects the formation and destruction of Cepheid progenitors and what effect this has on global Cepheid properties. We also present eight new systems composed of two Cepheids (only one such system was known before). Among confirmed SB2 Cepheids, there are also several wide-orbit systems. In the future, these may facilitate independent accurate geometric distance measurements to the Large and Small Magellanic Clouds.