Green card processing and H1 B amendment simultaneously


Recently my client changed with same employer. My employer has to file H1 B amendment and also initiate my green card processing. Since I’ll be receiving a new i797 after amendment, shall I wait for the process to complete before applying for green card as PERM would require me to submit i797? Can my employer start both the processes simultaneously?

Also, what happens if I have to get another H1 B amendment after the green card is started?

Thank you!