We present an interferometric study of the CO line emission in the HH 288 molecular outflow. The IRAM Plateau de Bure interferometer was used to obtain an 11-field mosaic covering the whole flow ( ~ 2 pc) with an angular resolution of about 3.5'' (7000 AU at a distance of 2 kpc). The data were complemented with short-spacings derived from IRAM 30-m observations. The exciting source of HH 288, IRAS 00342+6347, is a young (dynamical age of the outflow =~ a few 104 years) intermediate-mass (bolometric luminosity =~ 500lsun , envelope mass =~ 6 to 30msun ) embedded protostar. This source is likely to be an intermediate-mass counterpart of a classical Class 0 low-mass protostar. HH 288 is actually a quadrupolar outflow, and the angular resolution provided by the interferometric observations allows us to rule out models involving limb-brightened walls of a wide-angle single flow to explain such a morphology. The presence of two protostars in the central condensation is the most appealing explanation to account for the presence of the two flows. While the small East-West flow has a quite simple morphology and kinematics, the large North-South flow includes several overlapping structures, created by successive ejection events. Large collimated limb-brightened cavities are observed, with high-velocity material located along or near the flow axis. The internal structure of HH 288, including morphological coincidence between the CO and H2 emission, supports prompt entrainment at the head of large bow-shocks as the main formation process of molecular outflows from intermediate-mass protostars. Based on observations carried out with the IRAM Plateau de Bure Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain).