If the stepfather has a significant amount of time as her stepfather (~8 years or more) then my advice is for him to be the adult. If he has less than that, 5-7 yrs at the most, then I fear this situation will never get 'better'. She will always remember "that time before Rick" as the best time ever then Rick came along and just got in the way.
Of course the teen is asserting herself and trying to be free at a time when she's really too young to be so.
Part 1...
If he has any established authority, then I would say that he needs to use it. Stop playing the verbal volleyball that she suckers him into. He should stomp those arguments before they get started and lay down the law like a runway in the desert. Boom.
"This is the decision, this is what you're doing."
She'll hate it and she'll hate him the entire time that she abides by his statement.
The problem with this is that it will only work if
- He has established authority; that in the past she has listened and obeyed his statements.
- Real dad has never vetoed him and there's no danger of it.
- You support him 100% and have never vetoed him.
Part 2...
This must be followed up immediately.
I'm not going to deal with you if you're hollering and being like this. When you're ready to act like a human and talk to me person to person, we can probably work something out.
This will only work if he is ready to accept that she is her own person. That even at the still newbie age of 16, she is beyond being told what to do. Only thing anyone can truly do at this point is try to impart some wisdom and hope they follow it.
Bottom line
She's a biological adult and trying to figure out who she is and where she's going. She needs help, not orders.
He's an adult in the house. He needs to act like an experienced adult and treat her almost like he would someone new at work.
You, the mother, need to take a more pro-active role. It's difficult, and nobody is used to it or well practiced. Get in there, knock their heads together and make them both act like adults.
If he has no established authority, the only part of this that matters is the part where you take control. None of the rest of it will matter. In that situation, I would give completely different advice.
Hope I've helps.