We have some toys that are communally owned: well, basically all of the building toys. The wooden blocks, the MagnaTiles and some LEGO pieces. Plus the play kitchen, which started off as our son's but became communal property over time. I love these toys, because they almost never cause fights!
Then there are toys that are individually owned by one child, like specific LEGO sets, dolls, etc. These are highly contested, and can cause fights if one kid is playing with the other kids' toys!
Overall, I've come to realize over time that communal toys are the way to go, when possible. But most toys lately have been gifts, and it's kinda hard to make those communal. So we roll with it, and work with the kids to manage any conflicts that come up.
How do you manage the split between communal toys vs individually-owned toys?