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Tom Clancys The Division imposes limit on the amount of ammo a player can carry in addition to the medkits. The way to bypass this limit is to either get the Paramedic backpack or the Police backpack. Both of these are useful for carrying more items than intended by the game. If you have access to both of these backpacks, it is best that you keep them with yourself instead of selling them to vendors for some credit. You will be able to equip both of these at restock points to gain extra medkits and ammo for your weapons. To do so, you will need to equip each of the backpack and then restock yourself through each mission.

This appears to be more of a glitch so there is a high chance that this will likely get patched in a future update. It is still a great tip for now and should work until it is patched in the future.