Before I start talking about zz_addparty I'd like to mention that there are several console commands that may appear attractive at first to those who wish to exceed the 3 companion maximum cap, but which can damage your game. I've added warnings to their wiki descriptions, but I'll touch on them again briefly here.
This command has the very useful ability to open the partypicker anywhere, even in areas where it is normally locked. Unfortunately it also stealthily hires every single companion in the game, even if you haven't encountered them yet. This will break the plots for any character you haven't yet encountered. And unlike zz_getparty this command stays dangerous at least up until the end of the Landsmeet, and potentially the entire game if you kill, fire or choose not to hire any of the companions after they've been encountered. Stay away from it. It will nearly always damage your game, and you usually won't discover it until much later since those newly hired companions won't show up in the partypicker. If you want a script that will open the partypicker anywhere then either write your own, or ask me for mine. :D
This command will remove a party member from your active party. Sounds good. Unfortunately it also permanently fires them and you will no longer be able to select them in the party picker screen. While you can use zz_addparty to rehire them, any character development they've gone through will be lost. They'll behave as if they had never adventured with you before. As I will talk about in my next post, zz_addparty should be used to remove characters as well as add them.
This command adds Alistair, Morrigan & Dog to your party regardless of who is already in your party. If you already have 3 companions in your party, and none of them are Alistair, Morrigan, or Dog, then you'll end up with 6 characters. If Morrigan is already in your party, but the other two are not, then you'll end up with 5 characters as Alistair & Dog get added. It's certainly a quick way to add those 3 characters, but it's useless for the rest. And it isn't entirely without danger. The danger is if this command is used before Alistair, Morrigan and Dog are all recruited into your party because it will stealthily hire them even if you haven't yet encountered them. Given how early those companions are hired, and given that it's pretty rare for anyone to use this command before Lothering, this command is mostly safe. One exception is if a non-noble kills Dog instead of healing him. Using this script at any point afterward may cause Dog to appear later in the game despite having been killed.