The 170 occupants of the four vessels more than doubled the population of West Island, one of the Cocos's two inhabited specks of land.
No sooner were 32 Sri Lankans - rescued last weekend after crashing into a remote coral cay - transferred to Christmas Island on Tuesday than another group arrived to take their place.
The latest boat was carrying 35 people.
In the past, asylum-seekers trying to reach Australia have aimed for Christmas Island or Ashmore Reef, both nearer to Indonesia, the most popular staging-point.
But for people travelling from Sri Lanka or India, the Cocos - 600km from Christmas Island - are a day's less sailing.
Until last month, only two boats had attempted to reach the Cocos from Sri Lanka, one last year and one in 2010.
On the latter occasion, five people drowned while trying to swim to safety from their stricken vessel.
The Government is struggling to cope with the recent influx, with immigration staff and Australian Federal Police officers sleeping in tents or on the floor of the fire station.
The administrator of the Cocos, Brian Lacy, told ABC radio yesterday that officials were considering turning an old quarantine station on another island, West Island, into accommodation.