I agree naval power is probably the key here. He who controls the sea can come and go at will, bringing in vast resources to overwhelm the enemy.
I'm not an expert on the Ottoman navy. The empire's resources were vast and they were still advancing on land until the 1690s. So I suspect there is a theoretical possibility to be had.
The main problem with the resources was that they were all over the place: Syria, Rhodes, Albania/Italy, Crimea, problems in Walachia, potential danger of Hungarian attack, etc. The Ottoman empire of that time did not have too many quality troops, especially Janissary (according to
https://en.wikipedia.org/wiki/Janissaries, in 1484 their number was 7,841 and remained almost the same till 1540's). So, if they had been used on the numerous theaters, it would be 2 - 3,000 per place, which is not too much, especially taking into an account their tactical limitations: they were good in the sieges (on both sides of equation) but an absence of the pikemen made them vulnerable to the cavalry charges and in most of the famous Ottoman battles on the West they had been fighting defensively behind the earthworks, stockades, etc. Battle of Ankara demonstrated what could happen to them in an absence of a cavalry support. Sipahi were a good cavalry but they were light comparing to the Western cavalry of the XV century and, AFAIK (or judging by their performance in the XVIII century), not well-drilled to fight as an unit. In other words, no substantial (if any) advantage unless present in the big numbers but they were not in an unlimited supply and as I understand there were "specifics" of their deployment like limited time span (due to the need to oversee the field works in their estates). The rest were either troops of the vassal states (like Serbian knights at Ankara or Moldavians and Walachians at 2nd Vienna or the Crimeans) of various quality and sometimes questionable loyalty or the Ottoman irregulars.
As a result, there could be only a limited number of troops dedicated to the Italian front. They could grab some piece of a territory but I would not bet on their ability to maintain a long-term occupation, especially taking into an account that there were both Spanish and French interests in this specific area and that any disruption of a status quo could easily trigger the direct involvement of these powers.
The late 1400s doesn't seem as good a time as the 1500s, due to the speed of expansion being too fast. But the time of Muhtesem Yuzyil? Seems feasible.
I happen to disagree. In 1494 the French involvement into the Italian (specifically Neapolitan) affairs started and soon afterwards you have Spain (and then HRE) involved as well. Of course, combination of the conflicting French, Spanish, Italian and Ottoman interests in Naples is interesting but I have no idea how it could develop except that, most probably, there would be a temporary Christian alliance against the Ottoman followed by the "business as usual" mess.
And as far as Suleiman is involved, IMO the Ottomans already started lagging behind the Western counterparts tactically. Anyway, what Suleiman did in OTL looks like a much more sound strategy because attack on Hungary (and then on Vienna) did not involve the limitations related to a seaborne operation, allowed to deploy much more troops AND made obvious geopolitical sense while landing in Southern Italy was not solving any problems.
I've just conquered Sicily with the Ottomans in Empire Total War, so I might be a little biased
In 1837 Tsar Nicholas I decided to commemorate 25th anniversary of the Battle of Borodino. Under his personal command the reenacting troops gained an easy victory over the "French" and Nicholas was foolish enough to say: "here is how the real battle had to be fought!". To which one of his generals (a rare specimen who had a backbone) answered: "Your Majesty, you forgot that in this reenactment the troops and artillery had been shooting blanks and, most important, Napoleon was absent!" Happy future conquests!
