Witr is part of the night prayer, and it is Sunnah and it is the end of the night prayer, one Rak`ah with which one concludes the night prayers at the end, or in the middle, or at the beginning of the night after `Isha.

Pray Witr with the Imam, then you can pray Tahajjud after that and pray whatever Allah wills for you, two by two Rak`ahs, without repeating Witr. Another option is delaying Witr until the end of the night.