Your question reminds me of this other recent thread, is it you? If not, it is just very similar questions.
http://www.discovertuscany.com/forum/accommodation-tuscany/3224-villa-day-tuscany.html
You can definitely do it - but like I had posted on the other thread, you have to make some decisions to narrow down the search, there are way too many villas in Tuscany.
So first, where will you be - in Florence or Lucca on the day of the birthday?
How many people total?
All day or just partial day?
Do you want catering for a party or just a nice, sit down dinner?
Right now, your question is too general, there are villas that are just open for events so all services are external. Some are more like a hotel that offer both accommodation as well as the venue for events.... but might be too small for your group. They might work with specific chefs or catering companies so once you find the location, they can take care of the rest for you.
Until you give us more details, at the moment I'd recommend all closer to Florence:
Villa il Poggiale
Villa Dianella
Tenuta Quadrifoglio