Abstract We present new photometric and spectroscopic observations of SN 2019yvq, a Type Ia supernova (SN Ia) exhibiting several peculiar properties including an excess of UV/optical flux within days of explosion, a high Si ii velocity, and a low peak luminosity. Photometry near the time of first light places new constraints on the rapid rise of the UV/optical flux excess. A near-infrared spectrum at +173 days after maximum light places strict limits on the presence of H or He emission, effectively excluding the presence of a nearby nondegenerate star at the time of explosion. New optical spectra, acquired at +128 and +150 days after maximum light, confirm the presence of [Ca ii] λ7300 and persistent Ca ii NIR triplet emission as SN 2019yvq transitions into the nebular phase. The lack of [O i] λ 6300 emission disfavors the violent merger of two C/O white dwarfs (WDs) but the merger of a C/O WD with a He WD cannot be excluded. We compare our findings with several models in the literature postulated to explain the early flux excess including double-detonation explosions, 56Ni mixing into the outer ejecta during ignition, and interaction with H- and He-deficient circumstellar material. Each model may be able to explain both the early flux excess and the nebular [Ca ii] emission, but none of the models can reconcile the high photospheric velocities with the low peak luminosity without introducing new discrepancies.