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:
1- It is recommended for a Muslim to offer eleven rakahs in Tahajjud prayer.
2- However, it is permissible to offer as much supererogatory rakahs during the night as one can.
Answering your question, The Permanent Committee for Scholarly Research and Ifta’ in Saudi Arabia, states:
It was authentically reported that `Aishah (may Allah be pleased with her) said: The Messenger of Allah (peace be upon him) did not observe more than eleven rakahs (of optional night prayer), be it in Ramadan or any other month. (Abu Dawud)
Also, it is permissible for a person to offer as much supererogatory rakahs during the night as they like. When the Prophet (peace be upon him) was asked about night prayer, he said: (Optional) Night Prayer is two rakahs (units of Prayer) followed by two rakahs (and so on), and when one of you fears the break of dawn (Fajr Prayer), let them offer a single rakah to make the prayer they have offered witr (Prayer with an odd number of units). (Abu Dawud)
The Messenger of Allah (peace be upon him) also said: “The most excellent prayer after the prescribed ones is prayer during the night.” (Muslim)
The night prayer is to be concluded with witr by praying a single rakah.
Almighty Allah knows best.