So, why 4 characters in a party? Why not 6 or 8 or 10? Why is 4 "Full up" according to the potential party members. This is not really explained in the game. The characters just say you are full up so they can't join you.
Here's a story suggestion Larian could use in game to explain to the player why only 4 can be in a party at once, and if they add a few simple mechanics to the game it would work well:
1. Magic pockets. At some point in the prologue, probably in the first 2 chambers, a cutscene should show the MC finds a set of 4 magic pockets. These can be traded to new party members if they are swapped in. However, since there are only 4 pockets, it works best to only have 4 party members. The MC could even make a brief comment to that effect.
2. A cutscene upon gaining your fifth party member. During this scene, the MC asks the new member to join. The new member then moves to join the others but the MC is the one to suggest that the party size might be now too big. "Perhaps a smaller group would be better," the MC states. "We might draw too much unwanted attention with more than 4. Besides, we could use someone to stay and watch over the camp." Then another member like Astarion might say, "Oh! And maybe they could handle all the boring things for us, like fishing and gathering and cooking and cleaning. You know, the peasant tasks that unimportant people do." Then a party management window would pop up allowing you to choose who you want to keep in the party and who to send to camp.
3. Food, water, and camp maintenance. During the first night at camp, a quick tutorial could explain that anyone you leave at camp will spend their days finding food, water and taking care of other camp maintenance like cooking meals, etc. The more characters you have, the more food and water and camp maintenance will be needed to survive. Thus, a simple camp mechanic could be done where the player chooses which party members will join the quest and which will be assigned to camp duties. Camp duties would be gathering food and drink first, then equipment maintenance. If you don't leave enough people at camp to manage this, penalties start to occur.
So 6 total members? 4 in party and 2 at camp satisfies the requirements. Prior to 6 members, 1 at camp satisfies the requirements. So kinda a 1 at camp for every 3 total members. Later, when you get even more members, maybe then increase party size to 6 with the MC stating it might be good to now take more members with. So 8 members total, 5 in party and 3 in camp meets the requirements. 10 members, 6 in party and 4 at camp. Prior to having a full party of 4, the player could still leave 1 at camp if they didn't want to worry about finding food, etc. or weapon maintenance for that day. Otherwise, they'd have to find food and fresh weapons or suffer penalties.
Failure to meet the requirements, such as when you are first starting, would start with a lack of weapon maintenance. Nonmagical weapons should receive penalties if used and not left at camp to be resharpened and maintained by a camp party member. You certainly find enough weapons in the game, so why not a simple system of having party members switch out damaged equipment at camp leaving them with a party member to fix. If there is not enough party members assigned to camp, weapons and equipment don't get fixed. This makes storing more weapons and such at camp, instead of always selling, more meaningful so party members can switch out gear each day leaving damaged gear behind. I'm talking small penalties for damaged gear like -1 to damage or AC. Nothing major. Again, only nonmagical and only items that were actually used in combat. The penalty wouldn't apply until the next day and only if the damaged item was taken with to continue adventuring.
As the party gets even bigger, they really need more to remain at camp. If they don't, food is no longer provided by camp party members. And so, the party had best have gathered enough that day to compensate or suffer a penalty the next day on their questing. Again, I'm talking maybe a -1 to rolls for adventuring on an empty stomach.
Food should also spoil after a day or so, thus making finding fresh food in the game more important and so forth. Again, you find a lot of food in the game,, so why not?? This would make it even more important to gain party members and have them assigned to camp so you don't have to worry about these kinds of things while adventuring. Then it would make sense to have fewer in the actual adventuring party so the rest could handle the mundane tasks that are still necessary to adventuring. The bigger the party, the more people who are needed for camp maintenance so they all continue to have food and such to survive.
And, I mean simple mechanics. I wouldn't want this to bog the game down. Each new day, player gets a camp maintenance window. They pick who does what with defaults set to match what they did the previous day, and weapon swap would be a button the player hits, electing to swap out damaged items only for identical nondamaged items. One button, all swapped at once, and if there is no replacement, the player is prompted to pick a replacement from the collective inventories. And any spoiled food would just disappear from your inventories. No need to keep it around or micromanage it.