It is permissible in Islamic law for a person praying a voluntary (nafl or sunnah) prayer to be followed by another person who intends to pray in congregation. This is established by authentic evidence from the Sunnah. Ibn ‘Abbās رضي الله عنهما reported that he once stood to the left of the Prophet ﷺ while the Prophet was praying at night, and the Prophet ﷺ moved him to his right, indicating approval of being followed in a voluntary prayer (Sahih al-Bukhari, Sahih Muslim).

The scholars deduced from this and similar narrations that a person praying a Sunnah or nafl prayer may act as an imam, even if he did not initially intend to lead. The intention of leading the prayer does not have to exist at the beginning; it is sufficient that the follower intends to follow.

Therefore, when a brother joins you during your four rak‘ahs of Sunnah before Ẓuhr, your prayer remains valid, and his prayer is also valid. You are not required to stop your prayer, restart it, or change your intention. You should simply continue your prayer normally, calmly, and correctly.

However, it is important to note that this permissibility applies to voluntary prayers. Leading others in obligatory prayers requires more consideration, and differences of opinion exist regarding differences in intention between imam and follower in obligatory ṣalāh.