All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Prophet did not pray 20 Rak’ahs during Taraaweeh prayers, but rather prayed only 11 Rak'ahs as narrated by "'Aa'ishah who said that the Prophet never prayed more than 11 Rak’ahs in Ramadan or otherwise." [Al-Bukhari and Muslim]
But this narration does not mean that it is not permissible to pray more than 11 Rak'ahs for many reasons:
Firstly, this is a report about an act of the Prophet and this does not mean that the matter is restricted to that number. Indeed the Prophet specified the number of Rak’ahs prayed by night saying: "The prayers of the night are in twos (two Rak’ahs followed by two Rak’ahs and so on)." [Al-Bukhari and Muslim]
Secondly, it is confirmed that the companions used to pray 20 Rak’ahs Taraaweeh during the reign of the Caliphate 'Umar . This is the evidence of the scholars who hold this opinion, and this is the opinion of Imam Ahmad Ibn Hanbal, Ash-Shaafi'i, Ath-Thawri, and Ibn Al-Mubaarak and this is the famous opinion of the Maaliki School of jurisprudence. As-Saa'ib Ibn Yazeed said: "They used to pray 20 Rak’ahs during the reign of 'Umar in Ramadan." [Maalik]
Thirdly, there is no scholar in the Muslim nation who stated that it is an innovation or not permissible to pray more than 11 Rak’ahs. If any scholar says so in this century, then this is the first time that it is said and his statement will be rejected.
May Allaah have mercy on all of us.
Allah Knows best.