I have a large family by modern standards 4dc from infant to secondary school age. I can see the OP's point in some ways as I have friends with large families where I do think individuality is lacking - dc are seen as groups. I don't parent like that, as many larger families don't. I hope we do make it work but I'm sure like all parents I make mistakes sometimes too.
To answer your question, here's how I do it.
- Each dc has their own hobby or two that their sibling isn't part of. I have friends who have all 3/4/5 dc in same hobby and I've chosen not to go that route. Of course they all do swimming lessons but their main thing(s) is/are unique to them. It means when we are at a piano concert we are all there supporting 1 dc, cheering them on and celebrating them.
- I knew I wanted a large family and had a slightly larger gap than I would have if I only had 2 dc. This means they need me differently and it isn't a contest in the same way I found it was with my dc who are closer in age.
- Because of that larger gap I find it easier to do one to one or one to two. For example I took 2/4 to a museum recently, baby didn't come with us and teen slept in. Later that day teen and I sat together drinking coffee (they just discovered they love it) and chatting while baby napped, one dc was out and one dc was drawing an elaborate city of people.
- I find it easiest to spend time with the eldest and youngest. Youngest due to feeding and the fact we are home together until I return to work while all other dc's are at school. Eldest due to later bedtime, similar interest in things and they've always very much been a family person. I have to be much more intentional about the middle two. One doesn't want a lot of one to one time, and is happiest having you listen to them when they want to chat, but most of their free time they want with a good book, lego or their cousin a very similar age. The other loves Mummy one to one time (dc 3) and I try to make sure we have 1/2 a day one to one at the weekend together as well as a good 30-60 minutes after the baby is in bed and before their bedtime.
- Before dc 3 I really thought about what was important to me as a parent that I would want to continue and see as not negotiable even adding more children. Those are things I keep as key priorities.
How to do it all? Lists. For me it's knowing what needs doing when and sticking to that so that my 'free' time can be with dc. I make all our meals from scratch, am the only driver to do the ferrying to activities, have 2 dc with disabilities that require weekly therapies (physical, OT, feeding etc.). Once 4th came along I really noticed I couldn't do things I enjoy in the same way I could with 2 dc or 3 dc at a stretch. I really don't socialise, though I have good friends. I try to catch up with friends but it definitely had to change a bit now having a larger family.
I do far less parent & toddler groups now even tho I'm on leave and not back at work. Part of that is the extra demands on time of 4 dc and part of it due to our situation with disabilities that mean appointments. I find my days require me to be productive so that time when dc are with me I have time and space for them. I give each day a purpose and work hard to use my time wisely. I give myself one weekday to do something special with the baby, usually swimming and the library.
There are two things I definitely don't do as much as I did when I had 2 dc. First is volunteer at school (tho I still do, but I did much more when I only had 2 dc) and second is the frequency in which I their friends over. Having said that I think I did way more when dc 1 and dc 2 were little than most people I knew did when it came to having friends over. Never a weekend went by they didn't have at least 1 friend over. As for now, dc 4 is too young for friends over but with DC 3 part of the issue is our home just doesn't lend itself well for that now either, not enough space/type of space is too open plan. It is something I'm aware of and now baby is a bit older I'm giving myself a goal of setting up something every 2/3 weeks. In fairness, her 3 closest friends families rarely have friends over, maybe a couple times a year, so we still do more than they do, which I guess makes me feel a little better about it. Thinking about it, this year (2023) I've had friends of hers over who are twins, and 2/3 of her closest friends over once. Also took one to a trampolining place. So 4 times in 2.5 months. Not so bad, but again nothing like what I did when oldest 2 were that age.
I think you can parent a larger family well, but it's not a given. Just like having a baby in itself doesn't make you a great parent. All dc deserve a family life that isn't short changed, just like every child does. It's why even though logistically harder we continue with days out, family time, extra curriculars, one to one time daily, friend birthday parties (many large families cut these out completely), annual holidays (even if it's just camping) and even having friends over.