We report the spectroscopic confirmation and lens modeling of the complex strong-lens system J0233-0205, in which the deflector consists of a pair of galaxies at zd = 0.790 +/- 0.022, the background source lies at zs = 2.160 +/- 0.002, and the circularized Einstein radius is thetaE = 1.680 arcsec +/- 0.003 arcsec. Our lens modeling requires two lens components, namely two elliptical galaxies with Einstein radii of 0.669 arcsec +/- 0.002 arcsec and 0.735 arcsec +/- 0.002 arcsec, respectively, and a projected separation of 0.513 arcsec (about 3.832 kpc), as well as three source components: two disk galaxies separated by 0.4965 arcsec (about 3.712 kpc), plus a point-like component closely aligned with one of the disks. From a joint lensing and stellar-population analysis, we infer a total stellar mass within the critical curve of the lens pair of (1.956 +/- 0.418) x 10^11 solar masses and a total enclosed mass of (1.107 +/- 0.008) x 10^12 solar masses, corresponding to a projected dark-matter fraction of 82 +/- 4%. The stellar masses of the two lens galaxies are (8.548 +/- 2.128) x 10^10 solar masses and (1.525 +/- 0.295) x 10^11 solar masses, implying dark-matter fractions within the z-band effective radius of 57 +/- 11% and 70 +/- 6%, respectively. The small separation of the lens pair, together with its relatively high deflector redshift, makes J0233-0205 a potentially ideal laboratory for probing the mass distribution and dark-matter content of close galaxy pairs. In addition, the two disk galaxies and the associated point-like source make this system valuable for investigating the merger process in the source plane.