Magnetic, thermodynamic, neutron diffraction and inelastic neutron scattering are used to study spin correlations in the easy-axis XXZ triangular lattice magnet K2Co(SeO3)2. Despite the presence of quasi-2D "supersolid"magnetic order, the low-energy excitation spectrum contains no sharp modes and is instead a broad and structured multiparticle continuum. Applying a weak magnetic field drives the system into an m=1/3 fractional magnetization plateau phase and restores sharp spin wave modes. To some extent, the behavior at zero field can be understood in terms of spin wave decay. However, the presence of clear excitation minima at the M points of the Brillouin zone suggest that the spinon language may provide a more adequate description, and signals a possible proximity to a Dirac spin liquid state.