Question:

Is it an innovation to pray more than eleven raka'at as the prophet stated?

Answer:

I'm aware that it is the opinion of some scholars that praying over 11 raka'at is an innovation. Their evidence is based on the hadith of Aisha (radia allahu anha) that the prophet (sallah allahu alayhi wasalam) never went over eleven raka'at in Ramadan or outside Ramadan.

The reply to that is the prayer of the night in Ramadan (taraweeh) and outside of Ramadan is unlimited:
a) Because Aisha (radia allahu anha) spoke in what she knew before her, and possibly most of the prophet's prayer was 11 raka'at or when he was in her house he prayed 11. That is not to say he may have prayed in his other wives house on same nights or on different nights more than that.

b) Aisha (radia allahu anha) used to sleep as the prophet prayed, especially during her menstrual cycle. In fact, we know of the hadith where the prophet (sallah allahu alieh wasalam) used to pinch her to move her legs.

c) Just as Aisha (radia allahu anha) said the prophet's night prayer was only 11, we have other in authentic hadith that indicate the prophet's prayer was more than 11. In the authentic hadith by Ibn Abbas (radia allahu anh), he said, "The prophet never went over thirteen raka'at in Ramadan or outside Ramadan in night prayers."

d) The prophet (sallah allahu alieh wasalam) said, "The prayer of night is two and two if you fear fajer make witr."

The prophet did not limit the night prayer. The way it is worded in Arabic is that the prayer of the night is as though he is saying the prayer of the night is two and two and two and two….and so on, and if you fear fajer make witr. Had there been a limit he would have mentioned that in this hadith.

There are other additional hadith where the prophet (sallah allahu alieh wasalam) mentions the night prayer without a limit such as the saying "Whomever stays with his imam in night prayer (meaning taraweeh) until his Imam leaves, Allah will write him as though he prayed the entire night."

Note the hadith said until the Imam is finished which indicates and unlimited number of raka'at .

e) Umar (radia allahu anh), who is of the great khulafa, whose sunnah we may follow and who would never innovate, ordered prayer to be 11 raka'at in the hadith of aisha and ordered prayer to be 23 as well.

I think the best way to reconcile numerous ahadith would be that because of the hadith of Aisha (radia allahu anha) saying he only prayed 11, we pray 11 as it seems like the prophet did most of the time. However, we do not limit our prayer to 11 raka'at based on the other ahadith that indicate so.
The number of raka'at should not be a reason for disputes and fitnah among Muslims as is known to have happened among let us say- Hanafis who will not pray unless you do 20, or supposed Salafis who denigrate if one goes beyond 11 raka'at.

And, Allah knows best.