All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad
is His Slave and Messenger.
There is no harm in delaying for this short duration in order to complete your supplication, especially since it is only a brief time.
Shaykh Zakariyya al-Ansari
stated in al-Ghurar al-Bahiyyah, combined with the text of al-Bahjah al-Wardiyyah in Shafiʿi jurisprudence:
“It is permissible for the follower, after the imam makes the taslim, to occupy himself with supplication and the like for as long as he wishes, even if he prolongs it.” [End quote.]
However, some scholars hold that this is disliked. Therefore, if you were to make the taslim immediately after the imam and leave off the supplication in order to prioritize following the imam, that would be preferable.
Allah Knows best.