Should a traveler pray all the supererogatory and regular sunnah prayers that he used to pray in his home country?

The majority of scholars are of the opinion that it is desirable to perform supererogatory prayers while traveling, whether they are regular (ratibah) or other (non-ratibah) prayers. This is the madhhab of the Malikis and the majority of scholars. Their evidence for this includes numerous hadiths, such as the Prophet, peace and blessings be upon him, performing supererogatory prayers while on his mount, performing the two rak'ahs of Fajr while traveling, and performing the Duha prayer on the day of the conquest of Mecca with eight rak'ahs.

Ibn Umar and a group of companions differed on this, their argument being that the Prophet, peace and blessings be upon him, and Abu Bakr, Umar, and Uthman did not pray more than two rak'ahs while traveling.