The French coach had previously named 21 foreign-based players in his squad, but with the conclusion of the domestic season in Tunisia, nine players from the Tunisia Ligue 1 now have a chance to fight for places in the final 23-man squad for the tournament in Egpyt.
The nine players just added to the Tunisia provisional Afcon squad are Firas Chaouat, Nassim Hnid and Aymen Dahmen of Club Sportif Sfaxien as well as Wajdi Kechrida of Etoile du Sahel.
Five Esperance players - Moez Ben Cherifia, Ghailene Chaalali, Aymen Ben Mohamed, Taha Yassine Khenissi and Anice Badri - have also been invited.
The Carthage Eagles won their first pre-Afcon friendly against Iraq 2-0 on Friday.
The team will be up against Croatia on June 11 before going on to confront Burundi on June 17 before they finally head to Egpyt to challenge for the continent's top prize in football.
Coach Giresse's men will kick off their Afcon tournament against Angola in Suez on June 24, before facing the Eagles of Mali and then Mauritania in their final group game.