  Direct imaging of exoplanets represents a challenge for astronomical
instrumentation due to the high-contrast ratio and small angular separation
between the host star and the faint planet. Multi-star systems pose additional
challenges for coronagraphic instruments due to the diffraction and aberration
leakage caused by companion stars. Consequently, many scientifically valuable
multi-star systems are excluded from direct imaging target lists for exoplanet
surveys and characterization missions. Multi-star wavefront control (MSWC) is a
technique that uses a coronagraphic instrument's deformable mirror (DM) to
create high-contrast regions in the focal plane in the presence of multiple
stars. Our previous paper introduced the Super-Nyquist Wavefront Control (SNWC)
technique that uses a diffraction grating to enable the DM to generate
high-contrast regions beyond the nominal region correctable by the DM. These
two techniques can be combined to generate high-contrast regions for multi-star
systems at any angular separation. As a case study, a high-contrast wavefront
control (WC) simulation that applies these techniques shows that the habitable
region of the Alpha Centauri system can be imaged reaching at least $8 \times
10^{-9}$ mean contrast in 10\% broadband light in one-sided dark holes from
1.6-5.5$\lambda/D$.
