Is it possible that a group of person read the Qur'an in a high voice together at the same time?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Reading the Holy Qur'an and reciting it slowly and distinctly thinking about its meaning is one of the greatest deeds that bring the person nearer to Allah. Muslim narrated that the Prophet said: "Recite the Qur'an, for on the Day of Resurrection it will come as an intercessor for those who recite it. Recite the two bright ones, al-Baqarah and Surah al-Imran, for on the Day of Resurrection they will come as two clouds or two shades, or two flocks of birds in ranks, pleading for those who recite them. Recite Surah al-Baqarah, for to take recourse to it is a blessing and to give it up is a cause of grief, and the magicians cannot confront it".
Allah Says (interpretation of meaning): {And recite the Qur'ân (aloud) in a slow, (pleasant tone and) style.}[73: 4].
So, if one wants to get the reward of the recitation of the Qur'an, he should follow the way described in the sunnah of the Prophet and his companions as far as the Qur'an recitation is concerned.
As for the manner you described in your question it was not reported from the Prophet nor from his companions. In fact it is an innovation.
Imam Al Shatbi said: "The Bidaa (innovation) is something in religion that competes with the true religion. It is, sometimes, a behaviour that aims at overdoing some worships…" He gave examples of innovations like: sticking to a given manner of Dhikr (remembering Allah) in groups with a given tone …… etc. [Al Itissam 1/50].
From the above, we conclude that it is unlawful to get together and recite the Qur'an in the way you mentioned. But it is lawful that one of them reads and the others listen or that they read one by one.

Allah knows best.