Throw me some mechanics

Let's see...

for finding "things":

drawing cards:
1) at random from a face-up pile
2) at random from a face-down pile
3) selecting from memory from a face-down pile
3) selecting your choice from a face up pile
4) position related card drawing (i.e.- if you land on this space, draw XX type of card)
5) die-related card drawing (i.e.- whenever you roll a 6 on a die or any combination of dice, draw XX type of card)
6) from the top of a deck
7) your choice from among the top X cards of a deck
7.5) your choice by searching the deck
8) of a random type including "inert cards" that actually do nothing (every once in a while, you draw something useless)
9) as a reward for some action (i.e. - when you finish a quest, defeat any opponent, for each 5 points you acquire, etc.., you may do any or combinations of the previous 8 things on this list)
10) static incremental bonus (as with #9 above, each time you go fully around the board, each 5 points you acquire, etc...)
11) stealing from other players
12) any combination of any number of the previous 11 choices

I could easily knock off 12-100 more given any real amount of time, but without some sort of limiting factors, you could be talking about just about anything someone could imagine...

...and that's just for drawing cards. There are dice, physical miniatures, books, written pen-and-pencil games, gameboards (both static like Monopoly and fluid like Settlers of Catan), and contraptions (like Mouse Trap).

D&D has intangible items that you can "find" (by this I mean that there is no physical representation of them in the real world) using charts, tables and books by rolling dice alone.

rolling dice, having a board, how many of which types of whose pieces are in what combinations of spaces at what time can influence any or all of the above mechanics multiple times during any given game, and that is just for the card drawing mechanics I listed here.

You also haven't said whether or not you have a static pool of items to find (there are 7 in the game, find them all), or whether there are 50 to choose from which you could POSSIBLY find, and furthermore, whether you have a POSSIBLE pool, that from which only a handful are used during gameplay (there is a 50-card deck of items, choose 15 to play with for this game and set the rest aside out of the game - the object is to be the first player to find 6 of the 15 items).

As for ways to encourage co-op:

there are even more than that, given that you will likely have to COMBINE UNRELATED mechanics in order to accomplish it.

Do you have any input that is more specific than "give me some mechanics"...?

For combining item-gathering and cooperative play, I'm thinking some trade mechanics can do. Or getting items from other players directly, buying or giving away can work. For example, if you visit another player location (shop, town, space colony, whatever) you can be rewarded or acquire, some item. Maybe the other player can choose to offer you some particular item (that helps you do the thing he wants you to), thus becoming a motive to be cooperative.

Keep thinking!