Fiqh-us-Sunnah Volume 2, Supererogatory Prayer, Fiqh 2.114.

The majority of the scholars are of the opinion that it is not disliked to perform nawafil during the state in which one is shortening his salah. On this point, there is no difference between regular sunnah prayers and other nawafl.

Al-Bukhari and Muslim record that the Prophet made the ghusl in the house of Umm Hani on the day of the conquest of Makkah and then he prayed eight rak’at.

Ibn ‘Umar reports that the Prophet prayed while riding in whatever direction he was facing and nodding his head [i.e., for the movements of the salah].

Al-Hassan relates: “The companions of the Prophet while on a journey performed supererogatory prayers before and after the fard salah.”

Ibn ‘Umar and others are of the opinion that there are no nawafl, before or after the fard salah, except for during the middle of the night. He saw some people praying after the salah and said: “If I were to pray, I would have performed the whole salah [as obviously that would have taken preference]. O nephew, I accompanied the Messenger of Allah [on journeys] and he never prayed more than two rak’at until Allah took his soul. And I accompanied Abu Bakr and he did not pray more than two rak’at.” He also mentioned the name of ‘Umar and ‘Uthman, then he recited the verse: “Ye have indeed in the messenger of Allah a beautiful pattern (of conduct).” This is related by al-Bukhari.

Ibn Qudamah combines what al-Hassan and what Ibn ‘Umar say by concluding that al-Hassan’s report points to the fact that there is no harm in praying nawafil while travelling, whereas Ibn ‘Umar’s report points to the fact that there is no harm in not praying such nawafil.