Is it permissible for me to pray the obligatory prayer again with the intention of it being a supererogatory prayer after I have already prayed it as an Imam in congregation?

Repeating the Fajr prayer with another person is considered an act of charity (sadaqah) by some scholars. Your first prayer is the obligatory one that has fulfilled your duty, and it cannot be considered a supererogatory (nafilah) prayer. As for your intention that the second prayer be obligatory, this is correct according to some scholars, but others believe it is not permissible. Thus, the first prayer is the obligatory one, and the second is supererogatory, or one can intend it as a repeated Dhuhr prayer, and it is not a condition to intend it as an obligatory prayer.