We report comprehensive multi-wavelength observations of a peculiar Type Ia-like supernova ("SN Ia-pec") ASASSN-15pz. ASASSN-15pz is a spectroscopic "twin" of SN 2009dc, a so-called "Super-Chandrasekhar-mass" SN, throughout its evolution, but it has a peak luminosity M B,peak = −19.69 ± 0.12 mag that is ≈ 0.6 mag dimmer and comparable to the SN 1991T sub-class of SNe Ia at the luminous end of the normal width-luminosity relation. The synthesized 56 Ni mass of M56 Ni = 1.13 ± 0.14M is also substantially less than that found for several 2009dc-like SNe. Previous well-studied 2009dclike SNe have generally suffered from large and uncertain amounts of host-galaxy extinction, which is negligible for ASASSN-15pz. Based on the color of ASASSN-15pz, we estimate a host extinction for SN 2009dc of E(B − V ) host = 0.12 mag and confirm its high luminosity (M B,peak [2009dc] ≈ −20.3 mag). The 2009dc-like SN population, which represents ∼ 1% of SNe Ia, exhibits a range of peak luminosities, and do not fit onto the tight width-luminosity relation. Their optical light curves also show significant diversity of late-time ( 50 days) decline rates. The nebular-phase spectra provide powerful diagnostics to identify the 2009dc-like events as a distinct class of SNe Ia. We suggest referring to these sources using the phenomenology-based "2009dc-like SN Ia-pec" instead of "Super-Chandrasekhar SN Ia," which is based on an uncertain theoretical interpretation. a Nordic Optical Telescope (2.56 m) located at Roque de los Muchachos Observatory, La Palma in the Canary Islands; b du Pont telescope (2.5 m) located in Chile at Las Campanas Observatory; c New Technology Telescope (3.58 m) located in Chile at the La Silla Observatory; d One of the Magellan Telescopes (6.5 m) located at Las Campanas Observatory in Chile; e One of the Magellan Telescopes (6.5 m) located at Las Campanas Observatory in Chile