Is it permissible to pray four rak'ahs of the regular Sunnah prayers (regarding which it was stated: "Whoever prays twelve rak'ahs every day, Allah will build for him a house in Paradise") between the first and second adhan for Jumu'ah prayer?

According to the most preponderant scholarly opinions, Friday prayer does not have a pre-Dhuhr Sunnah. Rather, it is legislated for the worshipper to arrive early at the mosque and pray as many supererogatory (nafl) prayers as he wishes until the Imam ascends the minbar for the sermon. The hadith of Umm Habiba concerning the twelve rak'ahs of prayer does not pertain to Friday. The majority of Imams have concurred that there is no Sunnah prayer before it. What has been reported from some Companions regarding prayer before Jumu'ah is from the category of voluntary (tatatwwu') prayers, not a regular Sunnah (Sunnah Ratibah). It is most preferable for someone who comes for Jumu'ah to engage in prayer until the Imam emerges.