When considering doing a split from a very strong colony -----. The strong hive that I would like to split has four 8 frame mediums completely full of brood, honey and pollen.
Four medium = three Langstroth is not strong hive ant not at least very strong. It is good hive which will winter with 2 mediums. In pring that is good start and yu will see perhaps very good hive next summer.
If you split the hive it will be quite weak next spring and it is slow to develope.
If hive is completly full and bees get still honey the brood area will become smaller. You should arrange more room for laying. Normal way is to extract honey.
Just now I am in a hurry to clean honey from hives so my queens have room to lay wintering bees. After a month our hives have brood almost at all.