It can be tempting to take as many items as you can for yourself but this method of playing is quite unfair on everyone else and can actually be unhelpful in the long run. You should check to see how many items your team have on the HUD before picking up bombs, ropes or items. If you have say 4 bombs and another player had 1, its better to let them have the item.

Crates can be picked up before being opened, so consider picking it up and sharing it with a teammate you think might be struggling or who needs the item more.

This goes for Altar sacrifices as well. If you have the Kapala and put enough bodies on it to get some Royal Jelly, consider giving it to another team mate as you'll already have access to near infinite health. If they are stuck below you, you could consider using ropes to help them get back up to an Altar/ Shop.

Another thing to consider is any back item (Jetpack, Cape, Powerpack) you already have on your back can be dropped and given to another player by holding down and pressing the left bumper on controllers. Again, you might be more experienced than another player and giving them these items is sure to make their lives easier, especially if they have died and have no items when they come back.

If you come across 2 of the same back item, you can actually carry one on your back and carry the other in your hands. Use this to your advantage and bring the spare one to your teammate!

When using the Key to get the Udjat Eye, consider how many bombs you have. Another player might have more and it would probably be more sensible for them to take this item, as if you go to the Jungle they will know the exact location of the Black Market. Sticky paste is also best to be given to the player with the Udjat Eye.

You can help other players reach the location of the Chest by using some of your ropes and bombs to give them access to this area. Chances are, they may not have enough resources to reach it as all resources are shared between the entire party.

Same goes for the Ankh. The player that has this item will need all the help they can get surviving the levels to come if you want any chance of reaching the secret areas. Consider giving them Royal Jelly or the Kapala, if they die this item will be lost forever and cannot be claimed by another player! Check how much health you have before picking up this item, perhaps another player would be better suited to carry it.

For Tun's Moon Challenge, it is a very good idea to have one player buy entry and go dig up items and gold whilst the rest of the team clears the level and waits for them to finish. You will receive a clover for this challenge so you should have plenty of time to clear the entire level. Remember, the player with the least resources is gonna be the best candidate to complete this challenge so they can get more items!

For the second challenge, you will want all members of your team to attempt this if possible. As you can all pick up torches and light the fires to win the prize!

When another player is poisoned, try to find a Pet and get them out of the level as quickly as you can. Alternatively, if there is an Altar, you can stockpile bodies next to the Altar and get the player that is cursed/ poisoned to put them on the Altar themselves. This is because cures from Kali will only effect the person that makes the sacrifices.

SPOILERS AHEAD FOR GETTING TO A SECRET LEVEL:
If you have made it to the Golden City and have the Ankh, and a back item, always give the back item to your teammate before sacrificing yourself on the Altar. When you make it to the next level, your teammate will still have this item!

I think most people know these tips, but you can pick up players and jump to reach higher areas. As you jump, the other player can jump as well and should be able to reach very high areas.

Consider sharing Turkeys by riding one, jumping up to a high spot and then dropping the Turkey back down so the next player can use it to get up.

A player with a Jetpack, Spring Boots or Climbing Gloves can pick up a player and use these items to help them reach areas they wouldn't be able to jump to themselves.

I think this might just be a me thing, but please try to be considerate of other player's play styles! My play style is definitely explore everything before moving on so when another play makes a b-line for the exit and immediately ends the level, it can be very frustrating. Often in this situation, the player that took the exit too quickly is only making the game harder for themselves as I'll often have a crate to give them, a Pet or a Cursed Jar. When they've reached the next level, there could be a shop and a lot of the time the money that could have been made in the previous level would have been enough to purchase specific items.

On the topic of Shopkeepers… Please consider your teammates before killing a shopkeeper! Although it is easier to deal with the Shopkeepers with more players, some players may find it more difficult and I usually find that if each player is exploring the levels properly there will always be enough money to buy almost all items in a shop without upsetting the Shopkeeper.

Having up to 4 guns blasting off all over the place is a sure way to get your teammates killed, so if you do decide to take on NPCs with a weapon always consider the positions of your teammates.

Deciding if a player wants to take on a shopkeeper or not can be difficult if there is no voice chat. Try waiting for another player before taking out the shopkeeper and see what they do. They might end up buying the items instead. I also find ducking on the spot of an item is a good way to indicate to another player that you want them to buy a specific item.