Assalamualaikum. I once saw a person pray rawatib prayer before zuhr with 4 rakaats and 1 salam, claiming that he is on the chase of having the first takbir of the Zuhr prayer with imam. The question is, is it true that it is permissible to pray sunnah prayer with 4 rakaats and 1 salam? Hope for an explanation.
Sunnah prayer in 4 rakaats and 1 salam is permissible to be done. However, performing 4 rakaats sunnah prayer by dividing the two rakaats with one salam is more afdhal as there is an addition of intention, takbir, tasyahud (tahiyat) and salam which add to the rewards.
Alhamdulillah, praise and thanks to Allah for the countless blessings He has blessed us all with. Blessings and salutations to the Prophet Muhammad PBUH, his wives, his family, companions and all those that follow his teachings to the day of judgement.
Rawatib sunnah prayers are done in 2 rakaats according to a hadith narrated by Abdullah bin Umar R.Anhuma where the prophet PBUH said:
صَلاَةُ اللَّيْلِ وَالنَّهَارِ مَثْنَى مَثْنَى
(Voluntary) prayer in both the day and night is two at a time
Sunan Abu Dawud (1295)
This sahih hadith explains that it is prioritised (afdal) to perform 2 rakaats sunnah prayer with 1 salam whether it is performed during the day and the night. Therefore, sunnah prayer is prioritised to be performed with 1 salam for each 2 rakaats. However, if a person combines all rakaats with 1 salam, it is permissible.  (Refer Syarah al-Nawawi ala Muslim 6/30)
The opinion stating that sunnah prayer is divided into 2 rakaats with 1 salam is the opinion of majority scholars of the madhhab including mazhab al-Shafi’e.  (Refer Tuhfah al-Ahwazdi 2/416, 2/411)
Besides, for those intending to perform 4 rakaats sunnah prayer before (qabliyyah) the Zuhr prayer and after (ba’diyah) it, then he is encouraged to perform 1 salam for every 2 rakaats based on the hadith mentioned before. (Refer Majmu’ Syarah Muhadzzab 4/10) 
4 rakaats sunnah prayers before (qabliyah) the Zuhr prayer by dividing 2 rakaats and 1 salam causing the addition to the intention, takbir, tasyahud and salam. This is because the rewards of these actions given by Allah are depending on the amount of effort given. This aligns with the legal maxim which states:
ما كان أكثر فعلا كان أكثر فضلا
The more the actions, the more the rewards (Refer Al-Asybah wal-Nazhair, Al-Suyuthi ( 1/ 143).
This maxim is taken based on hadith narrated from A’isyah R.Anha where the Prophet PBUH said:
أَجْرُكِ عَلَى قَدْرِ نَصَبِكِ
the reward is equal to your hardship or your spending
Sahih Muslim (1211)
For more added information, kindly refer to the discussion on rawatib sunnah prayers which are muakkad and not muakkad on the following link:
In conclusion, 4 rakaats sunnah prayer with 1 salam before (qabliyah) the Zuhr prayer and after it (ba’diyah) is afdhal to be divided into 2 rakaats with 2 salams in which 1 salam is for every 2 rakaats. This is because, there is an addition to intention, takbir, tasyahud and salam which call for many additional rewards.
 Al-Nawawi, Muḥyī al-Dīn Yahyā bin Sharf (1392), Al-Minhaj Sharḥ Saḥīḥ Muslim, Beirut: Ihya’ al-Turath al-A’rabi . jld 6 p :30
 Al-Mubarakfuri, Muhammad Abdurrahman Bin Abdurrahim, Tuhfah Al-Ahwazi Bi Syarh Jami’ Al-Tirmidzi, Beirut: Dar Al-Kutub Al-'Ilmiyah, jld. 2 p: 416, 2 p 416, jld. 3 p :169.
 Al-Nawawi, Muḥyī al-Dīn Yahyā bin Sharf (t.t), Majmu’ Syarah Muhadzzab, Dar al-Fik, jld 4, p : 10
 Jalaluddin Suyuthi, Abd Rahman bin Abi Bakar (1990), Al-Asybah wal-Nazhair, Dar al-Kutub Ilmiah, jld. 1,p : 14