So I just purchased 2 core sets so we could play with 4 players. We ended up getting through The Gathering scenario and I can tell already I’ll want to pick up expansions. So does that also mean I would need to purchase 2 of each for an expansion (e.g. Dunwich Legacy, Path to Carcosa, etc.) to maintain a 4 player game? Does the same apply to the mythos packs?

It sort of depends. Each Mythos pack and Big Box expansion contains 2 copies of each player card. So, if you absolutely had to have each player able to have 2 of each card, then technically you would need 4x of each mythos pack and Big Box.

Realistically though, you are probably not running a team where you use 4 of the same class. That means there really isn't a lot of competition for cards, since each character's deck building requirements are different. I would think that 2x Core and 1x of every thing else is probably enough. I would definitely say just buy 1 of everything first, and if you find yourself making decks and you really are dying for more copies of a particular card, pick up a second copy of that pack.

I totally agree with @awe832 and just wanted to add that the BEST part of an LCG format is knowing what is in every pack. If your playgroup finds a Neutral card that more than one of you wants a pair of for your deck, you can just look up what pack it comes in and get that pack. I play with up to four investigators and I prefer restricting my available cards to the quantity in the 2 cores and 1 of everything else, but there are a few cards I'm tempted to have 4 of so multiple decks can utilize them.

It helps also to have invested players that are willing to buy their own copies so you don't have to supply everything for everyone. It can be a big ask, but it is a fun game (and if they like to solo at all, they can always solo play it themselves when others aren't available).

I supply the card pool for my whole group, once you get into Dunwich you really only need one of each expansion for 4 players. You may make some slight compromises here or there but as the pool of cards grows that becomes a smaller and smaller issue. Just avoid overlap where possible, I usually build 3 decks mostly from 1 class each (all guardian cards, all seeker, etc) and the 4th may use someone like Agnes if we're not running survivor or mystic already.

Perhaps a good idea if you want to make the plunge is buy the whole Dunwich cycle in one go if you plan on getting it all anyway. Your card pool will be in a really good place if that's not too expensive for you.

The card I want most to have multiples of is Charisma. It's in The Essex County Express pack. It's a permeant asset that allows you to field an additional ally. I think it is the most useful card across all characters (IMO) and the pack only comes with 2 copies. That said, it's a permanent, which means it's never shuffled and starts the game in play. As a result, we just proxy additional copies of the card. I think it's the only card we do that with.

The big overall answer is: NO.

You do not need to buy multiples of each expansion. They all contain 2 off every invesstigator card so you can build complete decks from them without issue.

The true answer is: Maybe.

Certain cards may find themselves to be popular in certain decks, I went all the way and got 4 core sets (Used on Ebay for example) to buff out my collection and then I went online to singles retailers and found a few copies of popular cards. Shortcut for example is very useful, Rite of Seeking may find its way into a variety of decks, everybody loves Lucky!

The game at this point is getting kinda big, and the initial bandwagoners are swapping out for other games since they've now experienced 3 campaigns, which means this is as good time to check ebay and see if you can find any collections to buy bulk. If you have just the 2 cores right now then a deal on "2 core + Dunwick" wouldnt be a far stretch.

or you can print the cards you need and put them in the protective sleeves using the back of the cards you don't need ...