Hello ,
Unfortunately, I can't answer that that easily for you. For us, it was said that it only works if both companies sign for their respective trades and thus are liable.
I find it quite odd that your house builder doesn't even sign for his own actions. That was a given with our provider.
I don't believe that TÜV or Dekra will also sign your building application, but I'm open to being proven wrong.
As a tip, you can look up the department for building applications at your responsible district office on the internet and call them directly. Alternatively, let the central office connect you. If anyone knows how they approve it, it's the ladies and gentlemen there. If that doesn't work, they can usually give you names of who can help you as the "overall construction manager."
I spent three quarters of a day on the phone until I got the tip to try directly there.
Good luck. And if you need someone to exchange ideas with (or to vent), feel free to get in touch.
Best regards, Sabine