Is it recommended to change one's place after having prayed the obligatory prayer and wishing to perform the supererogatory prayers thereafter?

There is no harm for the ma'mum (congregant) to perform nafl (supererogatory) prayers in the place where he prayed the fard (obligatory) prayer, and Umar (may Allah be pleased with him) did so. As for the Imam (prayer leader), it is mustahabb (recommended) for him to move from the place where he led the prayer, due to the hadith: "The Imam should not perform nafl prayers in the place where he leads the prayer."