Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is nothing wrong with the person who prays witr in the first part of the night or the middle of the night offering any nafl prayers he wants after witr, even though it is mustahabb for the last of his prayer at night to be witr. In this case, he should not repeat witr, rather the witr that he prayed at the beginning of the night is sufficient.
Answering your question, we would like to quote the following fatwa published on www.islaqa.info:
It was narrated that ‘AbduAllah ibn `Umar said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “Make witr the last of your prayer at night.” (Al-Bukhari and Muslim)
And it was narrated that that Talq ibn `Ali said: I heard the Messenger of Allah (peace and blessings of Allah be upon him) say, “There should not be two witrs in one night.” (At-Tirmidhi, An-Nisa’i, and Abu Dawud)
Ibn Hazm said in Al-Muhalla, 2/92-93:
Witr at the end of the night is better, but whoever prays witr at the beginning of the night, that is fine. It is permissible to pray after witr but one should not repeat witr.
An-Nawawi said in Al-Majmu`, 3/512:
If a person prays witr then he wants to offer a nafil prayer, etc. at night, that is permissible and is not makruh, but he should not repeat witr. The evidence for that is the hadith of `A’ishah (may Allah be pleased with her) who was asked about the witr of the Messenger of Allah (peace and blessings of Allah be upon him). She said: “We used to prepare his siwak (tooth stick) and water for wudu’ for him, then Allah would cause him to wake up at any time He willed at night. He would use the tooth stick, do wudu’ and pray nine rak`ahs, in which he would not sit except in the eighth, when he would remember Allah, glorify Him and make du`aa’. Then he would get up without saying salam, and pray the ninth rak`ah. Then he would sit down and again remember Allah, glorify Him and make du`aa’. Then he would say a salam that we could hear, then he would pray two rak`ahs after that, whilst sitting down.” (Muslim)
This is part of a lengthy hadith, which is to be understood as meaning that the Prophet (peace and blessings of Allah be upon him) prayed two rak`ahs after witr to show that it is permissible to pray after witr.
Almighty Allah knows best.