We study the multistability of fixed points for a dimerized system of Rydberg atoms driven by two laser fields and trapped in a two-dimensional (2D) square lattice. For identical driving fields, the fixed points of this system exhibit stable uniform, unstable uniform, stable nonuniform, or oscillating nonuniform phases in the presence of a bistable region. For different driving fields, however, all (stable, unstable, or oscillating) phases become nonuniform instead, which then results in two islets isolated from the mainland of Rydberg excitation. We also show that a tristable region may stretch out from the (nonuniform) bistable region near the islets, indicating that a richer phase diagram can be attained by tuning the Rabi frequencies and/or detunings of the driving fields. Last but not least, the fixed points can adiabatically evolve from the islets to the mainland but can not inversely evolve from the mainland to the islets.