The following are ways to obtain rare supply drops in Multiplayer mode:

Daily/Weekly Orders: Complete Daily Orders given by Major Howard to earn supply drops. Complete six Daily Orders in 24 hours to get a rare supply drop. Complete Weekly Orders to get rare supply drops; however, they are more challenging compared to Daily Orders.

Quartermaster Contracts: Quartermaster offers different rewards for different contracts -- each contract requires you to complete a certain action in a set time limit. As you scroll through them, keep an eye on the rewards, as not all contracts give supply drops.

Random Supply Drops: You can earn supply drops simply by playing multiplayer matches. There is also a chance you will get a random rare supply drop.