Is it permissible to pray the Sunnah of Dhuhr, both the pre-Dhuhr and post-Dhuhr, as four continuous rak'ahs?

The preferred way to pray the Dhuhr supererogatory (Sunnah (definition)) prayer is two rak'ahs at a time, separating each two rak'ahs with the salutation (tasleem), by analogy with the 'Asr supererogatory prayer. Nevertheless, there is no harm in not separating the rak'ahs and praying them as four continuous rak'ahs, although the former is more preferable. It was narrated from Ibn 'Umar that he would offer voluntary prayers during the day as four rak'ahs without separating them. This supports the permissibility of doing so, especially since the addition "wal-nahar" (and the day) in the hadith (definition) "The prayer of the night and the day is two by two (mathna mathna)" has been deemed weak by many imams of hadith.