  The coexistence of infinitely many attractors is called extreme
multistability in dynamical systems. In coupled systems, this phenomenon is
closely related to partial synchrony and characterized by the emergence of a
conserved quantity. We propose a general design of coupling that leads to
partial synchronization, which may be a partial complete synchronization or
partial antisynchronization and even a mixed state of complete synchronization
and antisynchronization in two coupled systems and, thereby reveal the
emergence of extreme multistability. The proposed design of coupling has wider
options and allows amplification or attenuation of the amplitude of the
attractors whenever it is necessary. We demonstrate that this phenomenon is
robust to parameter mismatch of the coupled oscillators.
