it looks like you're busy in planning your holidays in Tuscany and so far your plans sound great!
September is generally dedicated to wine festivals, since we have the Novello wine. All round Tuscany you can find many events and festivals. Most of them aren't advertised yet and you will be able to find more information later on, in early September.
Regarding Greve there is the 20th Chianti Classico Wine Festivalfrom September 9th to 12th.
The next weekend, from September 16th to 19th, in Panzano in Chianti there is "Vino al Vino" - Wine Festival.
On the same weekend there is also a nice market with antiques, crafts, food and wine, in Strada in Chianti. You can go to Panzano and Strada on the same day.
I also suggest you ask for more information about events when you'll be in Tuscany in September.
Well, I hope my suggestions helped you going on in your planning
At the moment the wine festivals I suggested before are the one I found information about.
Most of the local festivals aren't advertised before than a couple weeks from the event itself. So we can find information about more festivals in early September. Another thing is that most of events take place on weekends.
I always keep an eye on events in Tuscany and we publish the most interesting one on the Tuscany events calendar. Every week, generally on Thursday-Friday we also post on our blog "what to do on the weekend" with our personal plans and suggestions.
So I suggest you keep following us and post back your question in early September, so that we can have more info