Arc- and tail-like structures associated with disks around Herbig stars can be a consequence of infall events occurring after the initial collapse phase of a forming star, consistent with the observation of luminosity bursts. An encounter event of gas with an existing star can lead to the formation of a second-generation disk significantly after the initial protostellar collapse phase. Additionally, observations of shadows in disks can be well described by a configuration of a misaligned inner and outer disk, such that the inner disk casts a shadow on the outer disk. Carrying out altogether eleven 3D hydrodynamical models with the moving mesh code AREPO, we tested whether a late encounter of an existing star–disk system with a cloudlet of gas can lead to the formation of an outer disk that is misaligned with respect to the primordial inner disk. Our models demonstrate that a second-generation disk with a large misalignment with respect to an existing primordial disk can easily form if the infall angle is large. The second-generation outer disk is more eccentric, though the asymmetric infall also triggers eccentricity of the inner disk of e ≈ 0.05 to 0.1. Retrograde infall can lead to the formation of counter-rotating disks and enhanced accretion. As the angular momentum of the inner disk is reduced, the inner disk shrinks and a gap forms between the two disks. The resulting misaligned disk system can survive for ~100 kyr or longer without aligning with each other even for low primordial disk masses given an infall mass of ~10−4 M⊙. A synthetic image for one of our models reveals shadows in the outer disk similar to the ones observed in multiple transition disks that are caused by the misaligned inner disk. We conclude that late infall onto an existing star–disk system leads to the formation of a misaligned outer disk for infall that is inclined with respect to the orientation of the inner disk. Infall might therefore be responsible for observations of shadows in at least some transition disks.