I was in several campaigns like that. We had a large group with not-quite matching schedules, so we ended up having a "party" of 8 people, of whom 3-5 typically attended a given session. But occasionally, we'd have all 8 show up.

Honestly? It didn't work terribly well. That said, perhaps our failings can help inform your group.

1.) Quick Combat. Social and puzzle encounters worked all right, but combat was just awful. The long time between turns meant people kind of tuned out when it wasn't their turn, which meant that when it was their turn, they had to be reminded of the current situation before even considering what to do. Between this and other factors, a single 4-round combat encounter could take an hour or more to resolve. If you're going to have a group that large, you need to do everything you can to keep combat as snappy as humanly possible. Keep strict track of initiative so there's no confusion as to whose turn is coming up when, and insist that players act immediately when their turn comes up. With 8 people, there's plenty of time to do their thinking on other players' turns; if they hesitate, their character delays and the initiative order moves on.

2.) Balanced Combat. Furthermore, plan very carefully about what kind of combat you're going to run. 8 people is a formidable group, and it can be quite difficult to create an encounter that challenges them without seriously risking killing one or more PCs outright in every battle. Any encounter that can present a threat to a group of 8 PCs is likely to also be capable of reducing a couple of unlucky PCs to paste before the battle is decided.

If this is an experienced group running a large one-shot, the large size and mighty enemy groups may provide an exciting tactical challenge. If, however, it's at least partially new players or part of a serious campaign, your death rate is likely to be a problem.

In our case, the GM ended up basically saving everyone by GM fiat, or else having enemies stupidly abandon targets whenever they risked killing someone. It unfortunately combat less a challenge and more a quick-time-event, where the outcomes weren't decided by the players' actions in any meaningful way, but entirely by how deliberately stupid the chose to GM play the enemy.

I don't necessarily know the best way to do it, but I do know that our way was bad.

3.) Know the rules.

We had enough books for everyone (this was actually 3.5, so something like ~6 PHBs, 3 MM1s, and 3 DMGs between our 8 people, plus 1 or sometimes 2 of each more specialized book.) but actually looking things up ground things to a halt. If you're going to attempt to run a game like this, you need to be able to answer every question and resolve every issue more-or-less immediately. Anything less is going to quickly devolve into everyone looking through books when it's not their turn, rapidly disengaging. Or at least it did with us.

4.)Huge groups screw with the odds 8 PCs means 8 rolls on everything the group does together. Or 12 or more if half of them have familiars, cohorts, or animal companions who are rolling too. There will be a lot of natural 20s floating around, as well as a lot of terrible rolls. That means, acting as a group, they're going to make every perception check, and fail every stealth check. It also means they can get +stupidinfinity to "aid another" on individual checks if you aren't judicious. The game isn't designed for 8 people, and there are lots of cases where this shows. Not to mention the time it takes to even roll all those checks for everything.