A man was detained at Stansted Airport on Friday on suspicion of manslaughter and conspiracy to traffic people.
Two people from Warrington were also held on the same charges, while the lorry driver has been held on suspicion of murder since Wednesday.
The arrests came as efforts to remove and identify those who died continued.
Police officers have been seen at the home address of the arrested couple, a man and a woman, who are both 38.
The man arrested at Stansted Airport is aged 48 and is from Northern Ireland.
Police have been given extra time to question the 25-year-old lorry driver, Mo Robinson, of County Armagh.
The bodies of eight women and 31 men were found in the refrigeration trailer at an industrial park in Grays.
The trailer arrived in Purfleet on the River Thames from Zeebrugge in Belgium at 00:30 BST on Wednesday.
It left the port shortly after 01:05 the same day and the bodies were discovered at Waterglade Industrial Park about 35 minutes later.
It is believed a number of the people were from Vietnam, despite Essex Police initially saying the victims were Chinese nationals.
Families worried their relatives were in the trailer have contacted the BBC.
And VietHome, an organisation that represents the Vietnamese community in the UK said it had received photos of nearly 20 people reported missing, since the lorry was discovered.
The group said it began to receive reports of missing people on Wednesday. Those who have disappeared were aged between 15 and 45, it said.
The BBC spoke to the brother of Pham Thi Tra My, 26, who has not been heard from since she sent text messages on Tuesday saying she could not breathe.
"We are asking the British police to help investigate so that my sister can be returned to the family," he said.
The last message received from Ms Tra My was at 22:30 BST on Tuesday - two hours before the trailer arrived at the Purfleet terminal from Zeebrugge in Belgium.
Her family have shared texts she sent to her parents which translated read: "I am really, really sorry, Mum and Dad, my trip to a foreign land has failed.
"I am dying, I can't breathe. I love you very much Mum and Dad. I am sorry, Mother."
Relatives of Nguyen Dinh Luong, 20, have also said they fear he is among the 39 victims.
The Vietnamese Embassy in London has been in contact with Essex police since Thursday, a spokesman confirmed.
Liu Xiaoming, the Chinese Ambassador to the UK, said China was taking "firm and effective measures against human trafficking".
He called on the international community to "step up co-operation to crackdown on the crime of human trafficking".