I think if one was to open a Greek chain they would have to make it very classy looking. You would not want it to be cheesy at all. I would try to make it like you are on a Greek Island, have lots of pretty blues and other soft colors in the decor. Essentially don't have big pictures of the Acropolis everywhere and stuff like that.
I was fortunate enough to go to Greece this summer and the one thing I was afraid of was not liking the food. Ummm, I was totally wrong the food was amazing and I think would transition very well into a chain menu. I bet if there was a big Greek chain in my mall I would not have been afraid of the food in Greece. I mean the Greek chain menu can have really good Souvlaki (I did not know Souvlaki was essentially chicken on a stick before I went to Greece - people need to know these kinds of things because Souvlaki sounds kinda scary), Moussaka, Big Greek Salads, seafood, humus, steaks (because one of the best Steaks I ever had was on a cliff in Santorini), fried zucchini, something for everyone. The most important thing they should have on the menu is stuffed tomatoes because wow, those were the best things in the world and I do not even like tomatoes. Oh and they could make really fun drinks with Ouzo! That is something that could be so fun and different. They also could serve delicious breads with fun olive oil and other dips.
I think this chain would be very successful because it is different than so many of the other chain restaurants around. I mean look how successful My Big Fat Greek Wedding was. It made millions!
OK, so I guess you get my point. I am pretty sure there is a small, non corporate type of chain called It's Greek to Me which I found rather delicious when I went to it this summer down by the beach. That place gives me hope that one day there will be a major, upscale Greek chain in my neck of the woods.