  In a quantum critical metal, the electronic density of states, or
quasiparticle mass on the Fermi surface, is strongly enhanced through
electronic correlations. The density of states in the quantum critical
unconventional superconductor CeCoIn$_5$, can be readily accessed in the normal
state because all energy scales are small. However, the experimental challenges
associated with large nuclear specific heat and long nuclear spin-lattice
relaxation times have impeded unveiling a more detailed physical picture. Here
we report an extensive thermal impedance spectroscopy study of CeCoIn$_5$ that
assesses the density of states in two independent ways, via the nuclear
spin-lattice relaxation rate and via the specific heat. We establish that the
temperature- and magnetic field dependence of the nuclear spin-lattice
relaxation rate is determined entirely by the energy-scale competition near the
quantum critical point. In particular, mass enhancement is cut off at finite
magnetic fields. However, the specific heat measurements reveal excess entropy
in addition to that associated with the density of states on the Fermi surface.
This excess entropy is direct thermodynamic evidence for a "second flavor" of
fluctuating boson in CeCoIn$_5$. The electronic nature of this excess entropy
is evidenced by its suppression in the superconducting state. We suggest such a
multi-flavour character for a broader class of quantum critical metals.
