It is not permissible for the person who is praying behind the imaam to precede the imaam. It is haraam for him to move before the imaam, or to lag behind him so much that he misses the obligatory part of the prayer that comes next. The Prophet (peace and blessings of Allaah be upon him) said, “The imaam has been appointed to be followed. So when he says ‘Allaahu akbar,’ then say ‘Allaahu akbar,’ and when he bows in rukoo’, then bow in rukoo’.” The conjunction fa’ (translated here as ‘then’) implies following immediately, as is well known [in Arabic grammar].
Shaykh ‘Abd al-Kareem al-Khudayr
The idea of perfecting the prayer does not contradict the idea of following the imaam, so long as the imaam is unhurried in his prayer. There is no evidence for singling out the last sujood and prolonging this sujood but not the others, and it is not permitted to introduce innovations into the religion. And Allaah knows best.