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The new generation of multi-petawatt (PW) class laser systems will generally combine several beamlines. We here investigate how to arrange their irradiation geometry in order to optimize their coupling with solid targets, as well as the yields and beam quality of the produced particles. We first report on a proof-of-principle experiment, performed at the Rutherford Appleton Laboratory Vulcan laser facility, where two intense laser beams were overlapped in a mirror-like configuration onto a solid target, preceded by a long preplasma. We show that when the laser beams were close enough to each other, the generation of hot electrons at the target front was much improved and so was the ion acceleration at the target backside, both in terms of their maximum energy and collimation. The underlying mechanism is pinpointed with multidimensional particle-in-cell simulations, which demonstrate that the magnetic fields self-induced by the electron currents driven by the two laser beams at the target front can reconnect, thereby enhancing the production of hot electrons, and favoring their subsequent magnetic guiding across the target. Our simulations also reveal that the laser coupling with the target can be further improved when overlapping more than two beamlines. This multi-beam scheme would obviously be highly beneficial to the multi-PW laser projects proposed now and in the near future worldwide.