Italy and Greece trip doable?

It may be doable but that is a lot of 2 night stays with travel between. So basically 2 nights gives you one full day and an afternoon or morning in each location. Too much rushing around and too much travel stress in my opinion. Especially since you are going back to places in Italy you have been I would eliminate some places and add the time to other. I'd add time in Greece Especially since you have never been. Imho

Totally agree.... and people often try to apply French, Dutch or Itallian travel experiences to Grreece. No can do. Those countries have the benefit of dense & fast train networks that enable you to zip from one major city to another in 2-3 hours. Greece has virtuallly NO trains ... and to get from one island to the next takes as much time as gettting from one Country to the next, in most of Europe. Learn more about Greece (and it's worth it, a magical country) and you'll make more realistic & enjoyable plans.

I agree with both posters. Too much running around, split stays, and insufficient time in Greece. Why go back to Milan for a night before going to Venice? Take the train straight to Venice. Bam, you've freed up a night to spend elsewhere. Same with Rome. Go straight to Sorrento from Florence, then do all your Rome time after that. Instead of a stay in Athens on arrival, go straight to Mycenae after flying from Rome. Then do all of Athens at the end. Fly home from Athens on a multicity ticket instead of wasting yet another night in Milan just to catch a flight. Ideally, I think you need to add a couple more nights. Or if time is limited, consider eliminating one of your Italian stops.

Easyjet and Aegean Air have direct flights from Naples to Athens. Do that and you avoid the wasted time of back tracking to Rome.

And as already mentioned a multi city ( aka open jaw) routing of ORD-MXP/ ATH-ORD saves a lot more wasted time.

I second Cjean suggestion to do all the Athens days at the end.

For the Greek leg of your trip, on the day of your flight's arrival in Athens, take a bus to Nafplio or rent a car. Spend 3 nights in Nafplio, from where you can visit Mycenae and Epidaurus either with your rental car or on organized group / private tours if you don't have a car.
Then return to Athens by bus (or with your rental car) and stay there for 4 nights, which makes only 3 full days in Athens before taking a flight to ORD via Milan or another European city.

If you did like JoLui suggests for the Greek portion, you would have a very reasonable taste of Greece.

I have been to almost all the places you list for your Italian itinerary as have you it seems. I can't say that I see the charm of traveling that much to revisit quite briefly places you have been.

I would eliminate one location (Sorrento personally) and skip Milan. Consider an itinerary like this.
Lake Maggiore 3 nights
Venice 3 nights
Florence 3 nights
Rome 3 nights

2 nights might be enough for a revisit of Florence and you could add that night somewhere else or put Milan back in.

I concur with those tweaks, it could work. If I followed that Italy itinerary, I'd have to plop on a Greek island and not move for a week!

If you can take more time, as it seems to say in your initial statement, go ahead and do it--because why not?? But, here's another vote that unless there's something you need/want to see/do in Milan or Sorrento, ditch them and give an extra night to a couple of your other locations. Then, put all your days in Rome together. If you're already in Florence, Siena is well worth visiting (or vice-versa, in my opinion) and is an easy train ride away.

For Greece, totally agree with JoLui--But, I would vote that you rent a car at the airport and drive directly to Nafplio (Mycenae really isn't a location to spend more than a day, consolidate those days into Nafplio or Athens). The bus or tours are fine--but it's so much better with a car, Greece is very driveable and it's not expensive--very few places you can't take or park a car. The freedom it gives you is just the best, you can add other stops at will, and there are so many cool places you can go just off the main roads that will make this trip very customizeable. For example, I would have been so disappointed to drive back from Nafplio to Athens and not get to take a quick exit and visit Ancient Corinth/AcroCorinth--it's right there! IF you wanted to go on from Nafplio to Olympia, it's only about 2.5 hours. Then, when you're done roadtripping, take your car back to the airport, and ride the train into the city--driving or attempting to park a rental car in Athens is an experience that most would rather miss. If you can budget more time, you could visit at least one Greek island, perhaps in the Saronic, as those are quite close to the mainland--and a quick (and beautiful) slow-ferry ride away. You'll get lots of great advice here, hopefully, you'll have an awesome trip!