Italy is pretty much off limits, as that would directly cause a broad alliance of Christian Europe to take it back and then just keep matching forward.
Perhaps Sicily is in the cards, but certainly not mainland Italy.
I think Italy is doable, but not the whole Mediterranean for Roman Empire II; Rome had the advantage of being in the center of the Mediterranean, so transport costs to either end of the empire weren't too extreme, but Constantinople to Barcelona would make sustaining large forces on the other end of the sea very difficult.
It's easier than over land, but Roman historians have developed computational models to calculate transportation costs, and it's very difficult to keep them below prohibitive levels for supporting armies once you're talking opposite ends of the Mediterranean. Rome's central position was a fairly crucial advantage, and the Ottomans wouldn't really share in it. Algiers could be the base of a major galley campaign like Hayreddin's 1544 campaign of devastation along Italy, but I don't think it would be possible to subjugate mainland Spain. Such an effort would require a massive siege train and a full time army able to conquer Spain's major port cities, hold them against a massive counteroffensive, and winter on the opposite end of the sea from their base in Constantinople. The Ottomans historical amphibious offensives against the Spanish usually focused on territories they could isolate and strike with overwhelming force, like Malta or the North African garrisons. They didn't really mount campaigns of conquest and subjugation against i.e. Sicily; there were a few landings around Otranto, but nothing major really seemed to come of them.Sustaining forces by sea is easier than far inland. The Ottomans had difficulties reaching Vienna but no difficulty on reaching Algiers. Which is a base if they were to prepare a campaign.