We present new Gemini/GMOS optical spectroscopy of 16 extreme variability quasars (EVQs) that dimmed by more than 1.5 mag in the g band between the Sloan Digital Sky Survey (SDSS) and the Dark Energy Survey epochs (separated by a few years in the quasar rest frame). These EVQs are selected from quasars in the SDSS Stripe 82 region, covering a redshift range of 0.5 < z < 2.1. Nearly half of these EVQs brightened significantly (by more than 0.5 mag in the g band) in a few years after reaching their previous faintest state, and some EVQs showed rapid (non-blazar) variations of greater than 1–2 mag on time-scales of only months. To increase sample statistics, we use a supplemental sample of 33 EVQs with multi-epoch spectra from SDSS that cover the broad Mg II λ2798 line. Leveraging on the large dynamic range in continuum variability between the multi-epoch spectra, we explore the associated variations in the broad Mg II line, whose variability properties have not been well studied before. The broad Mg II flux varies in the same direction as the continuum flux, albeit with a smaller amplitude, which indicates at least some portion of Mg II is reverberating to continuum changes. However, the full width at half-maximum (FWHM) of Mg II does not vary accordingly as continuum changes for most objects in the sample, in contrast to the case of the broad Balmer lines. Using the width of broad Mg II to estimate the black hole mass with single epoch spectra therefore introduces a luminosity-dependent bias.