Lefkada is the island that’s not an island. You can drive to it across the causeway from the mainland, but it feels every bit an island. Aristotle Onassis bought the satellite island of Skorpios here as his own bit of getaway paradise. Beaches, windsurfing, boat hire, good food and wine are all here and there are few built-up package resorts. The main tourist area is centred on Nydri.
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.