Galaxy groups are a natural environment for the formation of elliptical galaxies. Despite this, most simulations to date have focused on mergers of isolated pairs of spirals galaxies. We have simulated hundreds of groups of spirals galaxies to test whether elliptical galaxies can form in the centers of such groups. We find that multiple dry mergers do produce elliptical-like remnants. These remnants have morphologies (Sersic indices and ellipticities) and scaling relations similar to nearby SDSS ellipticals. However, the less massive remnants are too large for their stellar mass and show very little rotational support, in contrast to e.g. ATLAS3D. Nonetheless, all remnants lie on a tilted fundamental plane relation with very small (<0.02 dex) scatter. These results suggest that dry and mostly minor merging - and not just gas dissipation - can have a significant impact on the structure of elliptical galaxies, although dissipation may dominate for less massive ellipticals.