The substantial influences of masonry infills used as partition walls on the seismic behavior of multistory reinforced concrete (RC) structures have long been recognized. Thereupon, in this study, considering open-ground floors due to a lack of infills (pilotis configuration), the structural pounding phenomenon between adjoining RC buildings with unequal story levels and unequal total heights is investigated. Emphasis is placed on the impact of the external columns of the higher structure, which suffer from the slabs of adjoining shorter buildings. The developing maximum shear forces of the columns due to the impact are discussed and compared with the available shear strength. Furthermore, it is stressed that the structures are partially in contact, as is the case in most real adjacent structures; therefore, the torsional vibrations brought about due to the pounding phenomenon are examined by performing 3D nonlinear dynamic analyses (asymmetric pounding). In this study, an eight-story RC frame structure that is considered to be fully infilled or has an open-ground floor interacts with shorter buildings with ns stories, where ns = 6, 3, and 1. Two natural seismic excitations are used, with each one applied twice—once in the positive direction and once in the negative direction—to investigate the influence of seismic directionality on the asymmetric pounding effect. Finally, from the results of this study, it is concluded that the open-ground story significantly increases the shear capacity demands of the columns that suffer the impact and the inelastic rotation demands of the structure, whereas these demands further increase as the stories of the adjoining shorter building increase.