Extreme debris disks (EDDs) are rare systems with peculiarly large amounts of warm dust that may stem from recent giant impacts between planetary embryos during the final phases of terrestrial planet growth. Here we report on the identification and characterization of six new EDDs. These disks surround F5-G9 type main-sequence stars with ages >100 Myr, have dust temperatures higher than 300K and fractional luminosities between 0.01 and 0.07. Using time-domain photometric data at 3.4 and 4.6$mu$m from the WISE all sky surveys, we conclude that four of these disks exhibited variable mid-infrared emission between 2010 and 2019. Analyzing the sample of all known EDDs, now expanded to 17 objects, we find that 14 of them showed changes at 3-5$mu$m over the past decade suggesting that mid-infrared variability is an inherent characteristic of EDDs. We also report that wide-orbit pairs are significantly more common in EDD systems than in the normal stellar population. While current models of rocky planet formation predict that the majority of giant collisions occur in the first 100 Myr, we find that the sample of EDDs is dominated by systems older than this age. This raises the possibility that the era of giant impacts may be longer than we think, or that some other mechanism(s) can also produce EDDs. We examine a scenario where the observed warm dust stems from the disruption and/or collisions of comets delivered from an outer reservoir into the inner regions, and explore what role the wide companions could play in this process.