Water megamasers from circumnuclear disks in galaxy centers provide the most accurate measurements of supermassive black hole masses and uniquely probe the subparsec accretion processes. At the same time, these systems offer independent crucial constraints of the Hubble constant in the nearby universe, and thus, the arguably best single constraint on the nature of dark energy. The chances of finding these golden standards are, however, abysmally low, at less than or similar to 3% overall for any level of water maser emission detected at 22 GHz and less than or similar to 1% for those exhibiting disk-like configuration. We provide here a thorough summary of the current state of detection of water megamaser disks along with a novel investigation of the likelihood of increasing their detection rates based on a multivariate parameter analysis of the optical and mid-infrared (mid-IR) photometric properties of the largest database of galaxies surveyed for 22 GHz emission. We find that galaxies with water megamaser emission tend to be associated with strong emission in all Wide-field Infrared Survey Explorer mid-IR wavelengths, with the strongest enhancement in the W4 band, at 22 mu m, as well as with previously proposed and newly found indicators of active galactic nucleus strength in the mid-IR, such as red W1 - W2 and W1 - W4 colors, and the integrated mid-IR luminosity of the host galaxy. These trends offer a potential boost of the megamaser detection rates to 6%-15%, or a factor of 2-8 relative to the current rates, depending on the chosen sample selection criteria, while fostering real chances for discovering. 20 new megamaser disks.