Since airline reservation requests are often made by city-pair (such as "show me flights from Chicago to Düsseldorf"), an airline that can codeshare with another airline for a variety of routes might be able to be listed as indeed offering a Chicago–Düsseldorf flight. The passenger is advised however, that airline no. 1 operates the flight from say Chicago to Amsterdam, and airline no. 2 operates the continuing flight (on a different airplane, sometimes from another terminal) to Düsseldorf. Thus the primary rationale for code sharing is to expand one's service offerings in city-pair terms to increase sales.
Of the above groups the Dodecanese probably constitute the best opportunity to mix islands between groups. You could, for example, take the Blue Star Ferries and map an island-hopping route that essentially heads in the same direction. In this way you could take in some of the Cyclades – Syros, Mykonos, Patmos, Naxos and some of the Dodecanese – Patmos, Leros, Kos, Chalki, and Rhodes – without any backtracking. Hellenic Seaways is another major ferry company whose routes you may want to explore.