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.
When the Jumu'ah (Friday prayer) is performed according to its conditions of validity, no Thuhr prayer should be prayed in addition to it. Doing so is considered a religious innovation. The Prophet said: “Whoever introduces to this matter of ours (Islam) that which is not part of it, it will be rejected.” [Al-Bukhari and Muslim]
However, if the Jumu'ah lacks any of its conditions of validity and if it cannot be performed again as Jumu‘ah, then it is obligatory on the person whose Jumu‘ah was invalidated for the lack of one of its obligatory conditions to pray Thuhr instead of it.
The Jurists also state that if Jumu'ah is prayed in the same area more than one time without necessity, the second Jumu‘ah is invalid and if two Jumu‘ah prayers are performed in the same place at the same time, then both of them are considered invalid.
Ibn Al-Qayyim said: “It is forbidden to perform it in more than one place in a given area except for a dire necessity. Now if they do, the valid Jumu‘ah is the one led by the Imaam or the one he permitted to be held. If both Jumu‘ah were permitted by the Imaam, then the second one is invalid and if they were both performed at the same time, they are both invalid.”
To conclude, know that performing both the Jumu‘ah and the Thuhr at the same time is something innovated in Islam and Thuhr should not be performed except if no Jumu‘ah is performed in the area.
As for continuously praying Thuhr after Jumu‘ah, then this is unlawful. If the reason for this is the invalidity of their Jumu‘ah, then they should correct what's wrong so that the Jumu‘ah becomes valid.
Allaah Knows best.