We have 6 kids, ages 4-14, and always go to Disney with my parents, so party of 10. Our strategies:
-We ALWAYS rent a villa offsite, usually Windsor Hills. For $200 a night, this year we are getting a 6 bedroom villa with it's own pool / hot tub, large kitchen & livingroom, games room and laundry. Not to mention the onsite amenities, massive resort pool and kids waterpark. You couldn't pay me to switch to a hotel room.
-We book a Disney campsite for 1 night at the beginning of our stay. We don't camp there, it's just for day use. For $70, this gives us 10 magic bands, free parking for all on the days flanking our reservation, and access to the 60 day fp booking window. See the "Throwaway Room" thread for advice on this.
-This year we are ordering our groceries from the Walmart Superstore 2 minutes from our villa. We will order online and pick it up on our way to check-in. We will make our own breakfasts at the villa, pack picnic lunches and our own waterbottles for Disney, and eat out 1 meal a day. This saves us roughly $700-$1000 in restaurant food / beverage costs for the 10 of us.
-We are a 24 hour drive from Disney, but we drive instead of fly every time. Even with seat sales, it's thousands of dollars for all of us to fly, verses a couple hundred bucks worth of gas. This allows us to have our own vehicles instead of having to rent one down there.
-We spend only 3-4 days at Disney and the rest of the week is spent going to the beach, lounging by the pool, etc. Saves money on tickets and give everyone some downtime.
Hope that was helpful for you! Have a great trip