  Mixing two chemical elements at the surface of a substrate is known to
produce rich phase diagrams of surface alloys. Here, we extend the concept of
surface alloying to the case where the two constituent elements are not both
atoms, but rather one atom (copper) and one molecule (fullerene). When
deposited at room temperature on a Cu(111) surface, fullerenes intermix with
the metal substrate. Surprisingly, 10 distinct copper-fullerene surface alloys
are found to coexist. The structure of these alloys, i.e. their composition and
commensurability relationship with the substrate, is resolved using scanning
tunneling microscopy and density functional theory calculations. This diversity
in the alloying process is associated to the multiple possibilities a fullerene
can bind to the Cu surface. The molecules are indeed found to have in-plane and
out-of-plane positional degree of freedom: the molecular alloys have elastic
in-plane properties and can buckle. In addition, the molecules can rotate on
their binding sites, conferring extra degrees of freedom to the system. We
introduce a competing-interaction energy model, parametrized against the
results of the \textit{ab initio} calculations, that describes well all the
phases we observe experimentally.
