  Over-luminous type Ia supernovae (SNe Ia) show peculiar observational
features, for which an explosion of a super-massive white dwarf (WD) beyond the
classical Chandrasekhar-limiting mass has been suggested, largely based on
their high luminosities and slow light-curve evolution. However, their
observational features are diverse, with a few extremely peculiar features
whose origins have not been clarified; strong and persisting C II lines,
late-time accelerated luminosity decline and red spectra, and a sub-day
time-scale initial flash clearly identified so far at least for three
over-luminous SNe Ia. In the present work, we suggest a scenario that provides
a unified solution to these peculiarities, through hydrodynamic and radiation
transfer simulations together with analytical considerations; a C+O-rich
envelope (~0.01 - 0.1 Msun) attached to an exploding WD. Strong C II lines are
created within the shocked envelope. Dust formation is possible in the late
phase, providing a sufficient optical depth thereafter. The range of the
envelope mass considered here predicts an initial flash with time-scale of ~0.5
- 3 days. The scenario thus can explain some of the key diverse observational
properties by a different amount of the envelope, but additional factors are
also required; we argue that the envelope is distributed in a disc-like
structure, and also the ejecta properties, e.g., the mass of the WD, plays a
key role. Within the context of the hypothesized super-Chandrasekhar-mass WD
scenario, we speculatively suggest a progenitor WD evolution including a
spin-up accretion phase followed by a spin-down mass-ejection phase.
