Relatives of Ryan Passey met with Justice Minister Alex Chalk this week to set out their arguments for why they believe juries should give reasons for their decision in the event of perceived "perverse" verdicts.
It was the first step in their bid to achieve what would be a landmark ruling for the criminal justice system in Britain.
Mr Passey, 24, was knifed at Chicago's in Stourbridge in 2017 and his family believe the man accused of murdering him was wrongly acquitted.
They are in the course of launching civil proceedings against Kobe Murray, who was cleared of murder. He admitted stabbing Mr Passey, of Quarry Bank, but said he did so in self-defence.
The family have also hired private investigators and hope fresh evidence could result in a re-trial.
Friend and family spokesman Jason Connon said he hoped their points were taken on board by Mr Chalk, following the meeting which included Mr Passey's father Adrian, their barrister Matt Stanbury and Stourbridge MP Suzanne Webb.
Mr Chalk acknowledged it would be a huge change for the criminal justice system but Mr Connon said that didn't mean they should not attempt to try and make it happen.
Mr Connon said: "It was the first meeting we've had with his office and in the time we had with him we put across our points quite forcibly.
"He respects a lot of what we're trying to achieve. He listened to the arguments from our barrister."
Asked whether he felt positive following the meeting, Mr Connon replied: "Cautious optimism. The journey we've been on, there's always a certain amount of caution but it went as well as we could have hoped for.
"I hope it's the first of many meetings and discussions going forward."
The family highlighted the battle of the Stephen Lawrence family and Ann Ming's campaign on double jeopardy in an attempt to show change can be achieved no matter how difficult it appears.
Mr Connon said: "He did mention it is a massive proposal for the criminal justice system. In his words, it would be revolutionary and the scale of the ask is considerable.
"We agreed but it doesn't mean it's not the right thing to do.
"If it wasn't for campaigners asking the Government to look at these laws people who were previously."