There is Algeria. And there is a reason why I named 1480. It was Mehmed II invasion of Italy. Had he not died he might as well had an Italian base making Tunis obsolete.
Well, the coastal part of Algeria had been taken by Barbarossa brothers (who kicked out the Spaniards) only in 1516 and conquest was not complete until 1518. But even with 2,000 Janissary he got from Sultan, Hayreddin hardly could do much more than just conquer the territory: a marginally successful expedition against Spain would require a considerably greater force.
How about 1543 when Barbarossa was operating out of Marseilles and Toulon (French-Ottoman alliance)? He had, presumably, up to 44 troops in his disposal but was operating mostly along the Italian coast: took Reggio Calabria, landed on the coasts of Campania and Lazio, threatened city of Rome and then switched Westward, taking Nice on behalf of the French king,
Francis I. In 1544 he continued his activities in the area until Charles V and Suleiman agreed to a truce. What if, instead of all of the above he attacked Mediterranean coast of Spain and perhaps even Cadiz? Of course, I have doubts about any serious
permanent conquest of the mainland but he could capture the Balearic islands and use them as a base for attacking the ports and controlling the traffic between Spain and Italy. If the later English activities (like raid on Cadiz) are indicative of anything, he probably could loot more than one Spanish port while the main Spanish forces had been busy fighting the French.