Only the Church Universal can decide how the Mass is “done.” That means that the Pope himself (or his delegate) must approve the ritual. The liturgical documents of the Church tell us how the petitions are prayed. The practice which you’ve described is not in harmony with those approved documents, so the answer is “no.”
Years ago, I attended mass at a parish that would allow people to add their petitions also. Every Sunday, there was a man that would say the same thing very loudly. Every week, you could see everyone physically tense up as this man began his NINETY second petition which would begin as a pro-life prayer, and end as a rant against “the bishops and clergy and all who by their silence give tacit approval…”
Some thought that 90 seconds was not too long…Obviously, I was one of the ones that thought otherwise and that’s when I timed it one day…
The priests allowed it for whatever reason. I found it very distracting and disturbing.
DISCLAIMER: Catholic Answers has turned over the archive to Catholic-Questions.org and no longer owns, manages, or moderates the forums. For additional apologetics resources please visit www.catholic.com.