On a week-long trip to Greece, if it is your first time in the country, you can visit Athens and one or two islands at most. Anything more will just give you a sense of rushing from place to place - hardly what you want for your vacation.
If you are returning to Greece and don't need to "do" Athens, you may be able to join three islands together during your trip, but that is the outside maximum. Stick with two if you can - you'll enjoy your time more and save on transit costs. Three that mix nicely due to transportation routes and schedules are Crete, Santorini, and Mykonos.
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