Hayne asked the securities watchdog to consider criminal charges against a number of organisations swept up in fees for no service scandals. Customers were being charged for advice they never received, in some cases even after they died.
Labor's other amendment would double the government's proposed cap on financial penalties for big businesses to A$525 million ($552,742).
In its current form, the bill sets one of the maximum civil penalties for corporations at 10 per cent of their annual turnover — with a cap of one million penalty units, which is about A$210m.
The opposition wants to increase that cap to 2.5 million penalty units, arguing the current legislation would only serve to protect the largest companies from facing the same financial risk as other firms when they engage in misconduct.
"The royal commission has shown that the big banks made hundreds of millions of dollars of profit from the fees for no service scandals, and the maximum penalty of A$200m that the government has proposed is simply too low," said opposition financial services spokeswoman Clare O'Neil.
"Labor will increase the maximum civil penalty to A$525m to ensure that banks don't profit from misconduct."
"After what's been exposed through the Royal Commission, Australians expect tough action on corporate crime, and Labor is delivering."
O'Neil said parliament needed to send a clear message to banks that they will face serious consequences for breaking the law.
"Many Australians feel that if they steal from a bank, they would go to jail, yet if the bank steals from them they get a bonus and a promotion. And we just can't allow that to continue," she said.
"One of the offences Labor is proposing to increase to a 15 year maximum sentence is the very same offence that Commissioner Hayne has recommended that the big banks be charged with for ripping off consumers through the fees for no service scandal."
There is, of course, a political aspect to this as well.
Labor has been hammering the government this week after frontbencher Christopher Pyne admitted it would not legislate in response to the royal commission until after the election, which is due in May.
"To change the laws around financial services and respond to the banking royal commission in the way that we wish to will take about 40 different pieces of legislation," Pyne said.
"So trying to do that in a rushed job to fulfil a political stunt that the Labor Party is trying to pull is no way to govern.
"And what we've tried to do in the last five years, of course, is to be sensible and methodical about the way we govern, and that's what we've done."
Labor says the delay is proof the government "cannot be trusted" on banking policy.
Meanwhile, Prime Minister Scott Morrison is resisting pressure to schedule more parliamentary sitting weeks before the election to deal with the royal commission's findings.
Labor needs the crossbenchers' support to win a vote on the floor of the House and force the government to schedule more time. But one of those crossbenchers, Bob Katter, has indicated he will not support the move.
Following yesterday's historic defeat on asylum seeker legislation, when Morrison saw his own government's bill amended by Labor and the crossbench against his wishes, he now faces a perilous dilemma in the Senate.
Does the government acquiesce, support Labor's amendments and implicitly agree that its own proposed penalties for banks are too weak? Or does it resist the move, and risk another embarrassing defeat?
