Is it permissible to praise Allah and make a brief supplication, moving the lips, while the imam is reciting aloud?

The fruit of prayer lies in humility and devotion (khushu'). Allah the Almighty says: "Successful indeed are the believers, those who humble themselves in their prayers." The most important things that help achieve khushu' are contemplating the Qur'an and remembrance of Allah (adhkar). The Prophet, peace and blessings be upon him, used to recite at length in his prayers; if he passed by an ayah of glorification, he would glorify Allah; if he passed by an ayah of asking, he would ask; and if he passed by an ayah of seeking refuge, he would seek refuge. This indicates reflection on the meanings of the Qur'an and interaction with them. It has been reported that the Companions used to supplicate after reciting certain verses. This interaction with the Qur'an and supplication can take place during recitation outside of prayer, or during voluntary prayers and night vigil (qiyam al-layl). However, in obligatory prayers, such supplications should not be made except in prostration (sujud), where supplication is not restricted. It was not the guidance of the Prophet, peace and blessings be upon him, nor of the early Muslims, to supplicate during the standing (qiyam) while reciting in obligatory prayers. Rather, one is commanded to listen attentively, though pondering with the heart is permissible.