The current game I am in has a large group, currently 6 players. The GM is getting a bit frustrated with challenging the group with encounters that aren't flirting with a TPK every round.
Party is currently level 3. For a Moderate encounter you have 80 + 20 +20 or 120 exp budget. That means either a single level 6 monster, a 5 and a 3, two 4s, three 3s, four 2s, or six 1s (with some mix and matching possible).
The problem is that it seems like the PCs can easily destroy this kind of encounter. I know that the single monster is not a good idea, 3 actions to their 18, but even two 4s (6 vs 18).
Level 3 PC has an AC of about 20 (10 + 5 armor/dex, 2 trained, lvl 3) and between 24 (elf wizard 10 con) and 60 (orc barb 18 con) hp, with an average of closer to 38.
A level 6 monster will have a +17 to hit and average of about 15 damage. This means they average 33.9 damage on two sings. Meaning they could easily drop a PC every round.
It would take this group of 6 PCs almost 4 round to take down this level 6 creature. Just on the math alone, this could easily be a TPK.
Does anyone have any suggestions on modifying the creatures to make this less deadly but still not a cake walk?
When adjusing for groups of different size, try adding or removing creatures if you can, instead of using stronger/weaker individual monsters.
So if you were going to use a level 5 (+2 vs the group) boss monster against a 'regular' party of 4, when adjusting for 6 characters it's usually better to add a level 3 one to help it instead of rising its level to 6.
Now, in some cases a single enemy makes for a more climatic fight; that's ok as long as it doesn't get too much ahead of the party (I would avoid level +4 or more unless you want a combat with really high stakes that will probably end with some dead PCs).
In your case, a group of 6 level 3 characters shouldn't be too much scared of fighting a single level 6 enemy; but of course it depends on the monster and the group composition, and what kind of approach they tend to have: anyone charging in on their own will probably get smashed as you predict. But with five more characters supporting them with healing, debuffs, flanking etc., the odds should be favourable.
For a Moderate encounter ... The problem is that it seems like the PCs can easily destroy this kind of encounter.
Yes, that is what moderate-threat encounters are for. The encounter is dangerous enough to feel like a real fight, but easy enough that any party with good tactics can easily win. Trivial and low threat encounters are more for flavor than challenge ("The door has a guard. He will be no trouble."). Moderate-threat encounters feel like a fight yet with only minor risk. Severe-threat encounters have a real risk that a party member will be knocked unconscious and risk death. Extreme-threat encounters have a risk of Total Party Kill.
I have been running a PF2-converted Ironfang Invasion adventure path for 7 players. My only problem with balancing the encounters is that my players invent better tactics faster than I learn them. Usually, I have to build a enemy force as powerful as them (extreme threat) to challenge them.
For a regular 4-member party, the Table 10-1 encounter budget works okay: 40 xp of enemies is a trivial threat, 60 xp is a low threat, 80 xp is a moderate threat, 120 xp is a severe threat, and 160 xp is an extreme threat. For a 6-member party, add 50% (two character adjustments) to the xp budget: 60 xp is trivial, 90 xp is low, 120 xp is moderate, 180 xp is severe, and 240 xp is extreme.
However, the creatures used to fill that xp budget make a big difference. A level+2 monster has the same xp as 2 level+0 monsters, but the fight will be qualitatively different. Monsters are designed so that PCs of their level have the abilities to fight them. Two levels further up, the monsters might have abilities tougher to handle, such as flying or regeneration or damage resistance. Even without new abilities, they will hit more often, hit with more crits, deal more damage, save against spells, dodge the party's strikes more often, and have more hit points to resist the damage that gets through. This superiority requires different tactics to level the playing field. And those tactics have to be more defensive, too, since the level+2 monster can deal killing blows more easily.
Level+3 monsters are worse. My PCs encounter those only at the end of a module. The first one, a 7th-level bugbear rogue against a 4th-level party, has handled by the liberator champion's Liberating Step nullifying the rogue's Twin Feint, so the enemy had to resort to less sophisticated attacks. Twin Feint is a rogue feat 2, so the party was expected to have a way to hand it. If the rogue had also learned Reactive Pursuit feat 4, then that tactic wouldn't have worked. The enemy rogue had soldiers with him to fill in the xp budget.
At the end of the second module, the 8th-level party faced an 11th-level adult black dragon. It would have been an interesting battle, with the party planning in advance and gathering anti-dragon weapons and finding a way to resist its Frightful Presence, because they had plenty of warning. However, the party also planned a diplomatic approach that worked, so the fight never occurred.
Frightful Presence is the kind of ability that can wreck a party if their Will saves are lower than expected.
It would take this group of 6 PCs almost 4 round to take down this level 6 creature. Just on the math alone, this could easily be a TPK.
Encourage them to take 6 rounds to take down the 6th-level creature by fighting more defensively. Take time to raise their shields. Have the two-handed-weapon fighter charge and then Step backwards so that the creature has to Move forward instead of getting all its Strikes. Have the wizard put a magical obstacle between the creature and the fighter to further mess with its attacks. Have injured PCs back away and used ranged attacks from a safe distance. Safety tactics prevent TPKs.
Combat via xp budget is more manageable if instead of using level+2 or level+3 monsters, the encounter uses level+1 and level+0 monsters, just more of them. My typical extreme-threat (280 xp due to 7 players) encounter is a squad from the Ironfang Legion with one level+1 commander (60 xp), two level-1 assistants (30 xp each), and eight level-2 soldiers (20 xp each) to fill out the squad to a challenging size. The encounter has death-defying risk, but the danger is spread thinner so that the party can save any PC who becomes overwhelmed.
If the module planned a level+2 monster as a moderate-threat challenge, don't replace it with a level+3 monster to keep the threat the same against 6 PCs. Instead, add a level+0 monster to the level+2 monster to fill out the xp budget. If no level+0 monster would make sense, then a second copy of the level+2 monster is better than switching to level+3. That raises the xp, but the battle will still be more appropriate for the PCs.
Furthermore, I have been talking about level+2 and level+3 monsters as if they were the only monsters that could nullify the party's favorite tactics, but that is an oversimplification. A level+0 monster with strange abilities, such as oozes, could mess up the party's tactics and devastate them. Learn to recognize in advance which monsters will befuddle the party.
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I also DM for 6 players, and rather than going solely off of the exp increases listed in the book, I take a proportion based approach. Making the big bad even bigger and badder will usually result in a wipe or close to a wipe even if it's in the exp budget because of how the math scales, so instead, I just multiply the number of creatures by 1.5; if theres an odd number, I slap elite adjustments on one or round up and give more loot.
If it's a boss fight, I either give the boss some more henchmen or make the environment worse by including terrain that prevents the whole party from bearing their power all at once, as well as hazards, rather than leveling the boss up. I also wipl sometimes let the boss prebuff if they have warning. The extra danger to them from a larger than 4 party is usually action economy, so the best way to accommodate that is nerfing the player's AE by making them burn extra actions to get in position, and/or giving the boss an action economy boost through prebuffs or traps; simple hazards in this situation basically act as free one off attacks for the boss
One trick I've used is adding the "level +0.5" to monsters by adding the HP and defence increases from the Elite template but not the attack and damage increases. This gives a monster a bit more staying power, without increasing the round by round threat it generates.
I call this template the Bruiser template in my head and it works pretty well. (I also use the opposite template to make enemies easier to drop whilst keeping them a scary threat, quite often to represent wounded or hungry beasts.)
PFS2 has started doing something rather similar, but only adding HP (a bit more than elite would have added), but not touching defenses or offenses on 'boss' encounters; mixed with adding minions and/or upgrading minions to full-elite. This has felt much better than the early days when they were a bit over-zealous in applying elite to solo monsters. The end result has been 1-2 rounds longer combat, without the boss being able to almost one-round any given PC.
Increasing level and all the associated stats that go with it such as attack bonus, AC, saves, perception, and the like is not the way to go.
The best idea is to add more creatures of the same level. This will let all of the player characters have something to deal with. It also means that each individual attack/defense roll will still be set correctly.
If you do have a solo or near solo enemy encounter, I would increase HP and add environmental features instead of adding a bunch of levels to the creature. This does have the problem of action balance. The party will have way more actions per round than the single enemy does. So that is something to be aware of. It would still probably be better to keep the original solo enemy as originally written and add lower level auxiliary creatures. It may not have quite the feel of the solo fight, but it will work out better for the game engine.
Be wary about adding more creatures with AoE effects like breath weapons or Trample. Those get boosted by having more targets, and if boosted again by adding more of said creatures, it can cause a bit too much destruction right off the bat which puts the party on their back foot...meaning the creatures will be more likely to recharge or catch enough PCs still clumped.
There might be similar force multipliers when adding Sneak Attackers or Pack Attackers, especially if their already of a mind to focus on one PC.
On the flip side, effects which grant immunity after saving (or sometimes even trying to save) will get that much weaker if the extra creatures' effects work less often.
I think thematic thugs w/ a decent Reflex save might be the best avenue. Or hindering traps as mentioned above for loner types.
Balancing by adding hazards is something that I never thought about, and a really nice idea.
That said, I usually have the opposite problem (3 PCs), which is probably more difficult to solve in general.