N.W.
I come from a big family, too. We only celebrate the kids' birthdays. Each family plans parties for their own children and we do something different every year. When my 4 kids were little, we'd have a party for each one individually and alternate between inviting extended family and same age friends. Same with my siblings, each year was different, sometimes a big family gathering, sometimes just friends and same age cousins. Then 3 of my siblings had girls within a month of eachother so one year we had a big family party for all 3 cousins at once.
I like that we can be flexible because as the kids get older, they want to choose what to do and who to invite to their parties. Since no one expects to be invited to every party, it gives each family the freedom to plan what works for each child on each birthday.