  A SQUID (Superconducting QUantum Interference Device) metamaterial on a Lieb
lattice with nearest-neighbor coupling supports simultaneously stable
dissipative breather families which are generated through a delicate balance of
input power and intrinsic losses. Breather multistability is possible due to
the peculiar snaking flux ampitude - frequency curve of single
dissipative-driven SQUIDs, which for relatively high sinusoidal flux field
amplitudes exhibits several stable and unstable solutions in a narrow frequency
band around resonance. These breathers are very weakly interacting with each
other, while multistability regimes with different number of simultaneously
stable breathers persist for substantial intervals of frequency, flux field
amplitude, and coupling coefficients. Moreover, the emergence of chimera states
as well as novel temporally chaotic states exhibiting spatial homogeneity
within each sublattice of the Lieb lattice is demonstrated.
