Silicene, the silicon equivalent of graphene, is attracting increasing scientific and technological attention in view of the exploitation of its exotic electronic properties. This novel material has been theoretically predicted to exist as a free-standing layer in a low-buckled, stable form, and can be synthesized by the deposition of Si on appropriate crystalline substrates. By employing low-energy electron diffraction and microscopy, we have studied the growth of Si on Ag(1 1 1) and observed a rich variety of rotationally non-equivalent silicene structures. Our results highlight a very complex formation diagram, reflecting the coexistence of different and nearly degenerate silicene phases, whose relative abundance can be controlled by varying the Si coverage and growth temperature. At variance with other studies, we find that the formation of single-phase silicene monolayers cannot be achieved on Ag(1 1 1).