We have spectroscopically identified 411 new E+A galaxies and candidates across 16 fields totaling roughly 480 square degrees in the Sloan Digital Sky Survey (SDSS). E+A galaxies are post-starburst systems that have undergone a significant burst of star formation within the past 1-2 Gyr and are now fully quenched, and comprise a small, transitional population that is key to understanding the transition from star-forming to quiescent galaxies. The survey has focused on four nearby rich clusters of galaxies and their surroundings: Virgo, Coma, Leo, and Hercules. The fields surveyed are 3° in radius, with the exceptions of the Virgo and Leo fields, which have radii of 5° and 1.3° respectively. We divide the E+A candidates into “blue” and “green” categories based on their broad-band colors. We find that the Coma Cluster has a very large number (18 blue, 139 green), confirming previous studies that have found an abundance of E+As and candidates in that cluster. Significant numbers of E+As and candidates are also found in and around the Virgo Cluster (23 blue, 91 green), the Leo Cluster (4 blue, 48 green) and the Hercules Cluster (4 blue, 74 green). Additionally, we found 10 E+A galaxies and candidates (1 blue, 9 green) located in the field regions rather than around the clusters. Among the clusters, we have further identified 657 “ambiguous” galaxies, which we describe as having spectral characteristics that suggest they are E+As but which we cannot confidently confirm due to either a low S/N ratio or the absence of components of E+A galaxy spectra. A small subset have available integral field spectroscopic data from the SDSS-IV Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) Survey; the MaNGA data are being used to confirm that these galaxies do not merely appear to be E+A only in their central regions, and are indeed fully quenched. Understanding the distribution and dynamics of E+A clumps has the potential to shed light on the evolutionary mechanisms present within nearby cluster environments. This work was supported by the Alfred P. Sloan Foundation via the SDSS-IV Faculty and Student Team (FaST) initiative, ARC Agreement SSP483, and by NSF grants AST-1852355, 1852360, 1460939, and 1460860 to the American Museum of Natural History and CUNY College of Staten Island.