Ciao Jakub,
Unfortunately, we don't have access to the accommodation we review and recommend, we can only suggest which ones might work for your needs and then you need to contact them directly to ask for availability. Most don't publish calendars that show dates they are still open as far as availability, so it makes it difficult to see and know where to focus your attention. With that out of the way, I highly recommend you take a look at these properties. The pages have a form at the bottom you can use to contact the owners directly.
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Villa Corsanello -
https://www.tuscanyaccommodation.com/villa-corsanello.html
While the villa is for 8 people, with 4 bedrooms, it is a full independent property in the middle of some of the most classic views of Tuscany and the extra person might be able to be fitted in as an extra bed.... not knowing whether there are any kids or all adults makes it hard to know whether it would work or not. So I've added this one because it's gorgeous, but all of the following are for 9 or 10 or 11 people, so should be the right size, all with their private pool.
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Osservatorio di Montignoso -
https://www.tuscanyaccommodation.com/osservatorio-di-montignoso.html
It is a whole villa divided over two apartments, for up to 11 people. So you could find out if the two apartments are free and thus have the entire villa and pool to yourselves for the week you are there. Keep in mind the owners do live on the property, but they tend to themselves while guests are present.
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Villa I Cipressini -
https://www.tuscanyaccommodation.com/i-cipressini.html
The entire villa is for 10 people, with own pool. Also in the Val d'Orcia, classic views!
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Villa Stolli -
https://www.tuscanyaccommodation.com/villa-stolli.html
Off the most beaten path but in a very panoramic location, very close to the main road that takes you everwhere. Plus, the villa is for up to 10 people so perfect for the entire group.
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I Cipressi -
https://www.tuscanyaccommodation.com/casa-vacanze-i-cipressi.html
Another villa divided into two apartments, by renting both you would have the space for all 9. With pool.
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Montrogoli -
https://www.tuscanyaccommodation.com/montrogoli-chianti-holiday-home.html
Villa for up to 12 people, in Chianti - own private pool.
I suggest checking them all out, contacting all of them for availability and cost for the week, then go from there. If you have no luck with these, let me know and I'll look for more to suggest!