  Multicolour light sources can be used in applications such as lighting and
multiplexing signals. In photonic and plasmonic systems, one way to achieve
multicolour light is via multi-mode lasing. To achieve this, plasmonic
nanoparticle arrays are typically arranged in superlattices that lead to
multiple dispersions of the single arrays coupled via the superlattice Bragg
modes. Here, we show an alternative way to enable multi-mode lasing in
plasmonic nanoparticle arrays. We design a supercell in a square lattice by
leaving part of the lattice sites empty. This results in multiple dispersive
branches caused by the supercell period and hence creates additional band edges
that can support lasing. We experimentally demonstrate multi-mode lasing in
such a supercell array. Furthermore, we identify the lasing modes by
calculating the dispersion by combining the structure factor of the array
design with an empty lattice approximation. We conclude that the lasing modes
are the 74th $\Gamma$- and 106th $X$-point of the supercell. By tuning the
square lattice period with respect to the gain emission we can control the
modes that lase. Finally, we show that the lasing modes exhibit a combination
of transverse electric and transverse magnetic mode characteristics in
polarization resolved measurements.
