All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible to supplicate in congregation on the condition that this is not taken as a regular habit or practiced as a Sunnah that is performed at particular and specified times. Therefore, if a person supplicates and the congregation says Aameen, and they do not take this as a habitual act, then this is permissible.
Moreover, Imaam Ahmad was asked: "Is it dislikeable for a people to gather and supplicate Allaah and raise their hands?" He replied: ''What I dislike for the brothers is to do that deliberately as a regular habit."
If this is taken as a habit and as a confirmed Sunnah which people do regularly and at a particular time, then it becomes an innovation in religion, because in such a case people would think that it is a confirmed Sunnah of the Prophet while in reality it is otherwise.
For more benefit on the ruling of supplicating in congregation after the obligatory prayer, please refer to Fatwa 86638.
Finally, it should be noted that it is not an obligation to start the supplication by praising Allaah and exalting the mention of the Prophet as it is not reported that the Prophet or any of his companions did so.