Can El Niño/La Niña occur again after normal state? As I know, El Niño and La Niña usually occurs alternatively, but is it possible that El Niño occurs again after El Niño and return to normal state?
If you look at the ENSO index record, you can see many instances of El Niño or La Niña occurring multiple times in a row. For instance, the period 1977-1983 and even after that is a succession of El Niño events with normal conditions in between and no La Niña period.

Multivariate ENSO Index (MEI) from NOAA