Is it permissible to change the intention of prayer from an obligatory (fard) to a supererogatory (sunnah) prayer or vice versa during the prayer, and which is better: to complete the prayer individually while worshippers join a new congregational prayer behind me, or to change my intention and join them in a new congregational prayer?

If two men find a person praying who has missed one or more rak'ahs (is a latecomer), it is better for them to form their own separate congregation to obtain the full virtue of congregational prayer. This is because completing the prayer behind the latecomer would mean each of them completes his prayer individually. However, if he is not a latecomer who has missed a rak'ah, then it is more appropriate for them to join him, so as to increase the number of the congregation. It is permissible for someone who has started praying alone to change his intention to a supererogatory prayer (nafl mutlaq) in order to join the congregation, under specific conditions.