  We present a study of the BAL outflows seen in quasar SDSS J1042+1646 (z =
0.978) in the rest-frame 500 -- 1050 $\r{A}$ (EUV500) region. The results are
based on the analysis of recent Hubble Space Telescope/Cosmic Origins
Spectrograph observations. Five outflow systems are identified, where in total
they include $\sim$70 outflow troughs from ionic transitions. These include the
first non-solar detections from transitions of O V*, Ne V*, Ar VI, Ca VI, Ca
VII, and Ca VIII. The appearance of very high-ionization species (e.g., Ne
VIII, Na IX, and Mg X) in all outflows necessitates at least two-ionization
phases for the observed outflows. We develop an interactive Synthetic Spectral
Simulation method to fit the multitude of observed troughs. Detections of
density sensitive troughs (e.g., S IV* $\lambda$ 657.32 $\r{A}$ and the O V*
multiplet) allow us to determine the distance of the outflows ($R$) as well as
their energetics. Two of the outflows are at $R$ $\simeq$ 800 pc and one is at
$R$ $\simeq$ 15 pc. One of the outflows has the highest kinetic luminosity on
record ($\dot{E_{k}}$ $ = 5\times 10^{46}$ erg s$^{-1}$), which is 20% of its
Eddington luminosity. Such a large ratio suggests that this outflow can provide
the energy needed for active galactic nucleus feedback mechanisms.
