Observational evidence indicates that the role of gas is secondary to that of gravity in the formation of the most luminous spheroids inhabiting the centres of galaxy associations, as originally conjectured in the late 80s/early 90s. However, attempts to explain the origin of the Fundamental Plane (FP) of massive early-type galaxies (ETGs) - a tilted version of the scaling relation connecting the size, velocity dispersion and mass of virialized homologous systems - based on sequences of pairwise mergers, have systematically concluded that dissipation cannot be ignored. We use controlled simulations of the pre-virialization stage of galaxy groups to show that multiple collisionless merging is capable of creating realistic first-ranked galaxies. Our mock remnants define a thin FP that perfectly fits data from all kinds of giant ETGs in the local volume, showing the existence of a unified relationship for these systems. High-ranked galaxies occupy in the FP different areas than standard objects, a segregation which is viewed essentially as zero-point offsets in the 2D correlations arising from standard projections of this plane. Our findings make a strong case for considering hierarchical dissipationless merging a viable route for the formation of the largest galaxies in the Universe.