Two first mates, one second mate and a chief engineer have been detained on allegations they failed to protect passengers, according to the Associated Press news agency.
The four crew members are also reportedly accused of abandoning the ship.
AP says prosecutors are considering whether to apply for a formal arrest warrant to allow for a longer period of investigation.
The ferry's captain and two other crew members have already been arrested on suspicion of negligence and abandoning people in need.
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Friday will be mostly dry with sunny spells for much of the UK. Temperatures will be mild across the country.