Is It Permissible to Make Du`a after the Jumu`ah Prayer?
Question

We pray the two Rak`ahs of Jumu`ah, then after that the Imam turns around and we all offer Du`a together. Is what we do correct?
Praise be to Allah.The believers should follow the example of the Prophet (blessings and peace of Allah be upon him) with regard to what he did and did not do. He should do what the Messenger (blessings and peace of Allah be upon him) did and refrain from that from which the Messenger (blessings and peace of Allah be upon him) refrained. Allah, may He be Exalted, said (interpretation of the meaning):
“Indeed in the Messenger of Allah (Muhammad) you have a good example to follow for him who hopes in (the Meeting with) Allah and the Last Day ...” [Al-Ahzab 33:21] 
Du`a by the Imam after an obligatory prayer – Jumu`ah or otherwise – with the congregation saying Ameen is something that was not done by the Messenger (blessings and peace of Allah be upon him) or by any of his Companions (may Allah be pleased with them). If it was good, they would have done it before us. 
Based on that, this action comes under the heading of reprehensible innovation. The Prophet (blessings and peace of Allah be upon him) said: “Whoever among you lives after I am gone will see great disputes; you must adhere to my Sunnah and the way of the Rightly Guided Caliphs. Hold on to it and cling fast to it. And beware of newly-invented matters, for every newly-invented matter is an innovation and every innovation is a deviation.” (Narrated by Abu Dawud, 4607; classed as authentic by Al-Albani in Sahih Abi Dawud)
And the Prophet (blessings and peace of Allah be upon him) said: “Whoever introduces something into this matter of ours that is not part of it, will have it rejected.” (Narrated by Al-Bukhari, 2697 and Muslim, 1718) 
Ash-Shatibi (may Allah have mercy on him) mentioned congregational Du`a after the obligatory prayer in his book Al-I`tisam (1/349-355), and explained that this is an innovation, because that was not done by the Messenger (blessings and peace of Allah be upon him) or by any of his Companions (may Allah be pleased with them) or any of the Imams (leading scholars) after them. 
What you must do is refrain from this innovation and strive to recite the Adhkar and Du`as that the Prophet (blessings and peace of Allah be upon him) used to say after the prayer. And whoever wants to offer Du`a may do so quietly. 
And Allah knows best.