In two words: Engage early.
If you engage early enough, you can’t go wrong. If you engage when you have no idea how to solve the issue, then you can’t go wrong.
If you engage with already a draft, it would take very, very high-skilled rhetoric to make this work. That’s the critical issue.
Of course, the more pressure you get from your internal and external stakeholders, the better, because doing this process will relieve you of that pressure. If one ministry or commission is met with undue pressure, usually it’s not really targeted at that ministry — It’s the stakeholders failing to communicate with each other.
The more pressure you get from more directions, the more likely it will work. That’s about it.