Bump up the number of opponents a bit. In general this means adding mooks. Because the amount of treasure and xp doesn't change (unless you change it) your PCs will be half a level behind and a bit short of gear, so it will tend to balance itself somewhat, especially against fixed DC problems. Besides, the PCs will make a noise, get in each others' way and soak up area attacks.
So if the encounter is nominally with a 3rd level wizard and 5 gnolls, it's now a 4th level wizard and 8 gnolls.
You'll probably want to be strict about rules like soft cover and precise shot so the casters and archers can't waste the opposition while the melee types hold the line.
You could always break the group up into two different campaigns and alternate every other week or run them on different days. Someone else could GM the other campaign to avoid overloading one person.
I had six players before we had one drop out. The APs are designed for 4-5, so I bumped some things up. For seven, I would have them make their characters one week/two-three days ahead of the first session and look at what you have.
This post made in the RotR thread makes a good point about how to do it.
I ran a game with 10 players for nearly three years. It can be very hard to challenge a group of that size because they have 2.5 times the action economy the game is built around. In order to challenge them, you have to upgrade your enemies in a way that doesn't make them outclass the group in terms of CR.
Standard party makeup is 1 Primary offensive caster, 1 Utility, 2 Primary melee.
For every primary melee character beyond 2, add 50% to each enemy's HP. (an average melee character is expected to deal between 25 and 75% of an enemy's HP a round. Adding 50% means the extra melee characters will be needed.)
For every Utility character beyond 1, add 1 enemy of CR equal to the average party level. (Utility characters are usually defined by buffing the party or controlling the battlefield. Adding extra baddies means they might not control everything, giving other characters something to do)
For each Primary caster, add +1 to enemy saves. (Monsters that fail saves against primary casters are usually out of the fight. You want to make it so the bad guys have a better chance of making their saves so that other casters have a reason for being there. Beware multiple casters spamming AoE control/damage spells. A few failed saves in a row, and the fight is over on round 1.)
Lastly, Maximize all monster HP.
This isn't a perfect formula for every group, but it works as a pretty good gauge as to how much you should boost encounters to still challenge the party.
Finally, and I can't stress this enough, mixed groups of enemies. If you run a bunch of enemies of similar types, they'll crush them. If you're running goblins, throw a pet giant scorpion in and some goblin dogs. If you're running giants, add giant eagles and summoned elementals. Make them diversify their tactics.
Do not simply tack on Hit Dice. It creates a ton of problems, mostly linked to special ability DCs and saving throws that outstrip what the party can handle. Adding Hit Dice will quickly neuter...
I didn't have to use this, since one of my players left, but it's still useful!
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Are you allowed to bump up the difficulty when running APs for PFS? I will run Snows of Summer at my FLGS as a PFS event. I won't know what PCs I get until I show up, but 6 characters are a distinct possibility. Are there rules for scaling up the encounters for >4 players? I am willing to tweak things on my own, but I don't want to invalidate the session from being PFS legal.
Are you allowed to bump up the difficulty when running APs for PFS? I will run Snows of Summer at my FLGS as a PFS event. I won't know what PCs I get until I show up, but 6 characters are a distinct possibility. Are there rules for scaling up the encounters for >4 players? I am willing to tweak things on my own, but I don't want to invalidate the session from being PFS legal.
I suspect if you're running sanctioned content as a PFS module, then no--you'd have to run as written but you may want to post this question on the PFS General Discussion or GM forum.