Is it permissible for the Imam to withdraw from his place during congregational prayer to allow a more senior Imam to lead, and if so, from which rak'ah does the new Imam continue?

If the person arriving is not the regular Imam of the mosque, it is not permissible to put him forward to lead the prayer while it is in progress, except in the case of an excuse. However, if he is the regular Imam, it is permissible for the one leading the people in prayer to step back and put him forward to lead the prayer, basing this on the action of Abu Bakr with the Prophet (peace be upon him). Nevertheless, it is preferable to avoid this to steer clear of differing opinions.