Q. can one read the sunnah after the azan of Jummah and also respond to the azan of the muazzin. What does one do when they have started their sunnah and Azan began thereafter/prior? (in office query)

A. Once the second azan of the Jummah salaah is called out, it remains incorrect to perform the sunnah. It would be best to shorten the sunnah if one has started it prior to the call of the Muazzin. If it is felt that one can complete the sunnah before the muzzin ends the azan, then one can complete the started sunnah. If the individual feels they cannot complete the sunnah, they can make the four rakats into two rakats and do a make up for the entire four rakats at a later point.

One would not respond to the masson duaa after the second azaan of Jummah. They would merely remain silient, and wait for the khutba to start.

Allah Certainly Knows Best.