When offering the Sunnah prayer before Zuhr, after the first two rak‘ahs, is it correct to change one’s place to offer the other two rak‘ahs, so as to earn reward, although it is the same type of prayer (regular Sunnah) – or is that applicable only between Sunnah and obligatory prayers?

Praise
be to Allah

In the answer to question no. 116064
we stated that it is mustahabb to separate between obligatory and naafil
prayers by speaking or moving to another spot. Some of the scholars stated
that the wisdom behind that is so as to increase the number of places where
the Muslim prostrates, so that they will testify in his favour on the Day of
Resurrection.

What is mentioned in the Sunnah is to move after an
obligatory prayer, for one who wants to offer a naafil prayer. There is
nothing in the Sunnah – as far as we know – about moving between two naafil
prayers. If a person wants to do so, such as in the case of one who is
offering four naafil rak‘ahs, and wants to move after the first two rak‘ahs
so as to increase the number of places where he prostrates, there is nothing
wrong with that.

Shaykh Ibn Baaz (may Allah have mercy on him) said, when
speaking about the four rak‘ahs before Zuhr:

The best is to offer them two rak‘ahs by two, because of the
saheeh hadith: “The prayers of the night and day are two rak‘ahs by two.” As
for moving forwards or backwards, or to the right or to the left, this is
mentioned in some da‘eef hadiths, and I do not know of anything to indicate
that doing so is Sunnah. Rather there are some da‘eef hadiths which mention
moving forwards or backwards, or to the right or to the left. Some of the
scholars said that this is so that these spots may testify to this act of
worship, but I do not know of anything concerning that that is proven to be
from the Prophet (blessings and peace of Allah be upon him). If someone
offers the regular Sunnah prayers in one spot, there is nothing wrong with
that, and I do not know of any evidence to suggest that it is mustahabb to
move to another spot for the last two rak‘ahs (of the Sunnah prayer),
whether he moves to the right or to the left, or forwards or backwards. But
if he does that there is nothing wrong with it.

End quote from Fataawa Noor ‘ala ad-Darb (10/296)

And Allah knows best.