In Imperial Brazil we had a fourth power, beyond the legislative, the judiciary and the executive, the moderating power, that belongued to the Emperor. The emperor could fire ministers, convoke the assembly, sanction the assembly's decrees and pardon criminals.
The idea was that the Emperor, being unelected and dynastic, would be above the petty squabbles and could intervene to limit them when those squabbles would threathen the stability of the empire. It worked well for two emperors, from 1822 to 1889.
It's said that the moderating power of the emperor saved Brazil from fracturing like the spanish viceroyalties fractured, even during the large scale rebellions like the ones in the Grão-Pará province and Rio Grande do Sul.