The galaxy SDSSJ095209.56+214313.3 (SDSSJ0952+2143 hereafter) showed remarkable emission-line and continuum properties and strong emission-line variability first reported in 2008 (Paper I). The spectral properties and low-energy variability are the consequence of a powerful high-energy flare which was itself not observed directly. Here we report follow-up optical, near-infrared (NIR), mid-infrared (MIR), and X-ray observations of SDSSJ0952+2143. We discuss outburst scenarios in terms of stellar tidal disruption by a supermassive black hole, peculiar variability of an active galactic nucleus (AGN), and a supernova (SN) explosion, and possible links between these scenarios and mechanisms. The optical spectrum of SDSSJ0952+2143 exhibits several peculiarities: an exceptionally high ratio of [Fe vii] transitions over [O iii], a dramatic decrease by a factor of 10 of the highest-ionization coronal lines, a very unusual and variable Balmer line profile including a triple-peaked narrow component with two unresolved horns, and a large Balmer decrement. The MIR emission measured with the Spitzer IRS in the narrow 10–20 μm band is extraordinarily luminous and amounts to L10-20 μm = 3.5 × 1043 erg s−1. The IRS spectrum shows a bump around ∼11 μm and an increase toward longer wavelengths, reminiscent of silicate emission. The strong MIR excess over the NIR implies the dominance of relatively cold dust. The pre- and post-flare NIR host galaxy colors indicate a nonactive galaxy. The X-ray luminosity of Lx,0.1-10 keV = 1041 erg s−1 measured with Chandra is below that typically observed in AGNs. Similarities of SDSSJ0952+2143 with some extreme SNe suggest the explosion of a SN of Type IIn. However, an extreme accretion event in a low-luminosity AGN or inactive galaxy, especially stellar tidal disruption, remain possibilities, which could potentially produce a very similar emission-line response. If indeed a SN, SDSSJ0952+2143 is one of the most distant X-ray- and MIR-detected SNe known so far, the most MIR luminous, and one of the most X-ray luminous. It is also by far the most luminous (>1040 erg s−1) in high-ionization coronal lines, exceeding previous SNe by at least a factor of 100.