H1B transfer when H4 pending & new employer is only filing H1 in premium & not H4

My wife entered the US on H4 on Jun-2020 and H4 visa/I-94 was valid until Sep-2020. My current employer filed an H1B/H4 extension in time for us in Jul 2020 and my H1B approval came through for 3 years but H4 extension for wife is still pending. Now I am switching employers. New employer will take care of H1B transfer only in premium & not H4. Once I join the new employer, my old employer will withdraw/revoke the H1b and so the previous H4 extension would probably be denied at some point and note that I-94 has expired for my wife.
Having said above for my wife, with

  1.  I-94 expired
    
  2.  H4 extension from previous employer still pending
    
  3.  and with only H1B transfer in premium with new employer, 
    

Can I file h4 extension via my own attorney for my wife separately after I get the receipt# of H1b transfer from my new employer OR you think it’s NOT possible because H1B transfer & h4 extension must be filed by the new employer concurrently. OR it’s better to join only after H4 approval comes through. I have already read on your forum that H4 is independent of H1B transfer which is ok but want to know the safest steps as current H4 extension is still in progress. Thanks for the help.

H4 can not be filed in premium. Your new employer should file the H4 extension in regular mode if at all they are filing. Refer to following link.
https://www.quora.com/My-H1-is-approved-but-my-dependents-H4-is-not-yet-approved-Their-I94-has-expired-Can-I-change-the-employer-without-putting-the-H4-status-in-risk

I agree that H4 can not be filed in premium but employer is not filing H4. Its doing only H1B in premium. So can I hire my own attorney to file H4 again separately once the receipt# of the new H1B is available.

my suggestion will be to file the H4 extension request along with your H1b transfer. Also talk with the company attorney and let him handle both H1B and H4 for consistency. You can pay from your own pocket if the employer is not willing to bear the cost of H4 .