The three are embroiled in a months-long scandal over their housing and travel expense claims.
For Duffy, it has been nearly a year since the first media report questioned whether he was eligible to claim an allowance for his home in Ottawa.
The RCMP is investigating the claims, but none of the three has been charged.
Brazeau faces charges in a separate matter.
The Senate sat Thursday from 2 p.m. ET to midnight, breaking for a couple of hours for dinner.
The government leader in the Senate, Claude Carignan, said there would be no Conservative Senate caucus on Friday, and that the Senate will resume sitting in the morning. A vote on some motions is possible.
Thursday's session showed increasing signs of a split in the Conservative caucus over Carignan's motions to suspend the three. Conservative Senator Don Plett said Thursday that the motions are premature, making it clear he will not support them.
Duffy, Wallin and Brazeau have all fired back at the bid by Conservative senators to have the three suspended without pay and benefits for inappropriately claiming Senate expenses.
Beside the three motions of suspension, there is a motion from Liberal Senate leader James Cowan to refer the suspension issue to a special committee for further study.Suggest a correction