No, Caliphs are not allowed to change the orders of allah nor the prophet.
However, the prophet (PBUH) specifically asked us to follow the 4 rightly guided caliphs(Abu baker, Umar, Othman, Ali) because they are the best people Islam has seen. The hadeeth found in At-tridmhi and Abu Dawud
The Messenger of Allah (PBUH) gave us a sermon by which our hearts were filled with fear and tears came to our eyes. So we said, "O Messenger of Allah! It is as though this is a farewell sermon, so counsel us." He (peace and blessings of Allah be upon him) said, “I counsel you to have taqwa (fear) of Allah, and to listen and obey [your leader], even if a slave were to become your ameer. Verily he among you who lives long will see great controversy, so you must keep to my Sunnah and to the Sunnah of the Khulafa ar-Rashideen (the rightly guided caliphs), those who guide to the right way. Cling to it stubbornly [literally: with your molar teeth]. Beware of newly invented matters [in the religion], for verily every bidah (innovation) is misguidance."
It was related by at-Tirmidhi, who said that it was a good and sound hadeeth.
As for the example you have given, check this answer:
Why did Umar (RA) forbid Mutah (temporary marriage) after the death of the prophet?