Increasing CR for more players

Question

I am currently running a short Pathfinder published adventure (We Be Goblins Too!) as an interlude between campaigns. For reasons not relevant to this question, I have 7-8 player coming each week. Not surprisingly, this has resulted in the combat being rather easy. I need to scale up the encounters, initially I was doubling the CR since I was doubling the number of players, but the initial low CR battle was way too easy that way. I have seen the rule of thumb being to add 1 CR per player past 4. However, since this is a low level campaign, that would mean the easy encounters triple in CR from 2 to 6 and the hard ones double from 4 to 8. That seems like a big leap.

I have a few specific concerns on how to do this:

1. Is the basic formula I suggested reasonable? Should I be adding 3-4 to the CR of the encounters to adjust them for 7-8 players?
2. More enemies vs harder enemies, which is better? More enemies has the problem of slowing down combat even more than it currently is. Harder enemies seem to get swarmed by the PCs and get taken out before they have a chance to do anything.
3. How do I keep the flavor of the battle when I am scaling the encounter up so much? For example:

   In the original campaign, a lot of the enemies are farm animals. There aren't many CR 6 farm animals.

4. Can I have stealth with this many people? With this many players someone pretty much always rolls high on their perception, meaning even enemies with a +10 stealth are likely to get spotted. Similarly, if they try and sneak anywhere, someone is going to roll low on their stealth and get spotted. Should I just give up on stealth as an element of this game?
5. In the future, would it be easier to just level down the players instead of leveling up the encounters. For example would it be fair to have my 7-8 players be at level 2 instead of the 4 players at level 3 it was designed for? Is there a formula for leveling the players down?

Note: I am aware there is already an RPG stack exchange question on scaling up encounters. However I don't think it addresses my problem for a few reasons. 1) It is a smaller scaling task (6 players instead of 8). 2) Most of my questions above were not addressed. 3) A lot of the answers focused on the fact there were a lot of inexperienced players where as all of my players are very experienced and some are super into character optimization. 4) That was for 3.5e where as this is Pathfinder (I know it is crimson not red, but still).

Note 2: For all of you that might point out "the system wasn't made for this many players", yes thank you, I know. We have a temporary situation we are solving with this short campaign, but it is a situation which does reoccur for us periodically. I am looking to make the best of this non-ideal circumstance, and I would rather keep all my friends around and engaged than spurn a few for my convenience.

Answer 1

I had a clarifying realization some years back that changed how I think about the problem of scaling past 6. It's just semantics, but I find it useful. The semantic/realization is that you've gone from a group to a horde. Hordes can overcome problems groups can't because they simply overwhelm the problem with their sheer numbers. You see that by having your horde waltz through challenges built for their character level.

The problem I found with scaling for a horde is that anything that can challenge a horde finds it trivial to remove a single member. i.e. something big enough to challenge your 8 players is going to find it trivial to kill at least one of them while they're taking it down. This adds a dimension to those fights that are rarer with smaller groups--finding themselves on the losing end of a fail cascade as key party members get taken out. This is why simply adding CR for each extra player breaks down past 6.

Which means that your problem is at least a bit insoluble (which is why people often answer that the game isn't designed for parties that large). For many years (12ish) I was in a group of players that varied between 8 and 11. So if you're still determined to try, here are some suggestions we had success with in a large group:

1. Break initiative into groups by rolling the monster init and then having an "above x" group and a "below x" group. Let your players self-optimize timing (who goes in what order) and realize that your monsters are going to be doing that, too (going all at once). It works with monster clusters, too, if for example, you have a big-bad with mooks (breaking down into three initiative groups). What this does more than streamline the flow of play, though, is bring everyone in a group together for the action as they plan what they'll do (as opposed to waiting for their initiative on an individual basis).
2. Develop a tolerance for characters falling to challenging foes. Recognize it's gonna happen and either manage resources for bringing them back from the brink (post-fight, possibly) or get used to the character turnover. You can DM-rule this with a handy party artifact or just have everyone bring a spare character for when their current one dies. Different groups have different preferences, but if they want a challenge, the game design means that they're fragile and their number will sometimes come up. You can lessen this somewhat if you house-rule that actual death is twice Con because they're just that cool.
3. Concentrate on story if your group will support it. Most combat encounters will become trivial with your group, so save combat for when it's really important. One way to do this is to just skip the trivial encounters with "yeah, you swarm these guys, what do you want to do with the corpses?"
4. Have only the x (two, most likely) most reasonable candidates roll for skill checks. Perception, diplomacy, bluff, etc. That helps the probability problems with a group that large (for most skill checks).
5. For stealth, I've had some success with a "how many succeed" metric. So all 8 roll stealth, for example, and if more than half succeed, then the party succeeds. The in-game theory to support this is the stealthy guys pointing out pitfalls and scouting ahead, etc. "psst, armor guy, don't step on that twig." That they're helping each other makes sense, at least to an extent. Yeah, it's not great verisimilitude, but it makes for much better game flow and most groups will go with it.
6. Scaling CR is going to suck. You can kind of develop a feel over time given a relatively consistent group, but it's still going to be more art than science--not least because some monster features will play havoc with CR at scale (like high-damage attacks that will decimate your lower-level-than-designed characters). Sometimes they'll blow through something you thought would be tough. And sometimes they'll fall to something you thought they'd handle just fine. The problem is that the price of failing is much higher for reasons mentioned above. I found it useful to have fail contingencies ready for the really big encounters (I don't like killing off player characters unless I can find an emotionally-resonant story hook). Vague mysteries can resolve for both good and ill in key moments and make you look like a GM genius if you set it up right. But again, that's more art than science...

Okay, all that said, there's a reason the above is past-tense. In the end, I chose to break off because it's just not as fun. We eventually morphed into two groups and the gaming is so very much better. The social cost of doing so was non-trivial, however, so I understand if you want to try to make this work.