The debate will culminate in a vote, expected to stretch into the early hours of Thursday, on whether to investigate each of the 10.
Under Greek law, parliament must first investigate allegations against lawmakers before they can be stripped of immunity and prosecuted by judicial authorities.
The discussion comes after Prime Minister Alexis Tsipras' government formally requested the procedure last week, citing testimonies from a judicial investigation into bribes Swiss drug-maker Novartis allegedly paid to boost the sales and prices of its products in Greece.
Tsipras' left-wing Syriza party cited the witnesses as claiming Novartis set aside more than 1 million euros to bribe Greek officials. It quoted allegations from one of the witnesses that a senior Novartis official in Greece delivered a suitcase of cash to the prime minister's office in 2013.
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All those implicated have denied any involvement, and at least four have filed criminal lawsuits against the protected witnesses. They have accused the government of using the judiciary for political aims and say the fact that the allegations are made by people whose identities are kept secret calls into question their reliability and motives.
The others include five former health ministers, one of whom Dimitris Avramopoulos is currently the EU's migration affairs commissioner. Current Bank of Greece governor Yannis Stournaras served as finance minister in Samaras' government from 2012-14 before moving to the central bank post.
Samaras, Avramopoulos, former health minister Adonis Georgiadis and former finance and deputy prime minister Evangelos Venizelos, who is also among the 10, have all filed lawsuits against the witnesses in recent days.