Forensic experts in Austria are carrying out post-mortem examinations on two babies found at an apartment block in the southern city of Graz.
People left candles at the scene of the shocking discovery
The two bodies were found wrapped in plastic and hidden in a freezer.
Two other babies, whose bodies were found entombed in buckets of concrete, were too badly decayed for the authorities to find out how they died.
Police have arrested a woman aged 32 - thought to be the mother - and her 38-year-old partner.
Police Lieutenant Colonel Werner Jud told the Austrian media that the possibility of more bodies being found at the site could not be ruled out.
"We are trying to determine the woman's past," he told Graz's Kleine Zeitung newspaper.
"Where did she live? Who were her acquaintances? Did anybody know about the pregnancies? These are the questions we're trying to answer."
The first body was found last week - reportedly when a tenant went to get an ice cream for his daughter. Later another body was found in the freezer.
The third and fourth were in plastic buckets filled with concrete in a garden shed at the residence, about 200 km (120 miles) south of Vienna.
Two of the bodies were found hidden in the garden woodshed
The woman, a bookkeeper, is reported to have admitted killing the babies in despair after giving birth.
Police have been questioning her in an effort to find out what happened. She has told investigators that she gave birth to the children in a bath, but could not remember what happened next.
The suspicious deaths are believed to have taken place over a period of three years.
The woman's partner is said to have denied knowing about her pregnancies. DNA tests are being carried out to find out if he is the father.