A third ship of the Conte Di Cavour class, would not have mattered much, as this class of ships was the first to be modernized in the 30's and appearently less succesfull than the Andrea Doria's, given the later's different scheme. Even the eventually pressence of the first dreadnought; Dante Alighieri, propably refitted as well, would not have made things much differnt, as the strategi was more to blame in WW2 for th Italians, then the number and quality of its ships.
A different and more agressive Commander of teh Regina Marina would have made little else too, as the combined command between Regina Marina and Aeronautica was missing. Simmilar to the problems in Germany between Luftwaffe and Kriegsmarine, the Italians had no real cooperation between the two armed forces, making operations in the Med. problematic at best. Since the Mediteranean Fleet of admiral Cunningham always included at least one aircraft carrier, as well as aircraft supporting from both RAF and FAA on landbases in the Eastern Med, Gibraltar and Malta. As long as there was nothing done about the British pressence in the air over the battle erea, the chances of the Regina Marina were little better than in the OTL.