This paper presents the first effort to Extend the Investigation of Stellar Populations In RElics (E-INSPIRE). We present a catalogue of 430 spectroscopically confirmed ultra-compact massive galaxies (UCMGs) from the Sloan Digital Sky Survey at redshifts $0.01< z< 0.3$. This increases the original INSPIRE sample eightfold, bridging the gap with the local Universe. For each object, we compute integrated stellar velocity dispersion, age, metallicity, and [Mg/Fe] through spectroscopic stellar population analysis. We infer star formation histories (SFHs), metallicity evolution histories (MEHs) and compute the Degree of Relicness (DoR) of each object. The UCMGs, covering a wide range of DoR from 0.05 to 0.88, can be divided into three groups, according to how extreme their SFH was. The first group consists of 81 extreme relics ($\text{DoR}\gtrsim 0.6$) that have formed the totality of their stellar mass by $z\sim 2$ and have super-solar metallicities at all cosmic epochs. The second group ($0.3\lesssim \text{DoR}\lesssim 0.6$) contains 293 objects also characterized by peaked SFHs but with a small percentage of later-formed stars and with a variety of MEHs. The third group ($\text{DoR}\lesssim 0.3$), has 56 objects that cannot be considered relics since they have extended SFHs and formed a non-negligible fraction (${>}25$ per cent) of their stellar mass at $z< 2$. We conclude that the most efficient method of finding relics is to select UCMGs with a combination of large velocity dispersion values (as already found by INSPIRE), super-solar metallicities and high [Mg/Fe].