Megamaser disks provide the most precise and accurate extragalactic supermassive black hole masses. Here we describe a search for megamasers in nearby galaxies using the Green Bank Telescope (GBT). We focus on galaxies where we believe that we can resolve the gravitational sphere of influence of the black hole and derive a stellar or gas dynamical measurement with optical or NIR observations. Since there are only a handful of super massive black holes (SMBH) that have direct black hole mass measurements from more than one method, even a single galaxy with a megamaser disk and a stellar dynamical black hole mass would provide necessary checks on the stellar dynamical methods. We targeted 87 objects from the Hobby-Eberly Telescope Massive Galaxy Survey, and detected no new maser disks. Most of the targeted objects are elliptical galaxies with typical stellar velocity dispersions of 250 km/s and distances within 130 Mpc. We discuss the implications of our non-detections, whether they imply a threshold X-ray luminosity required for masing, or possibly reflect the difficulty of maintaining a masing disk around much more massive (>10^8 Msun) black holes at low Eddington ratio. Given the power of maser disks at probing black hole accretion and demographics, we suggest that future maser searches should endeavour to remove remaining sample biases, in order to sort out the importance of these covariant effects.