Relatively simple idea; the player could push and pull carts with items and players in them.
This would be used when the player has yet to obtain a usable car, but they still might want to transport a large amount of materials.
So essentially, if a player finds a shopping cart like this:
The shopping cart could be loaded with crates full of materials, or smaller singular items, like logs.
Shopping carts could also be used to carry players around; maybe your friend broke his leg, and can’t keep up with you, so load him onto the cart to keep him off his feet. The speed of the cart will also depend on the strength of the player pushing, and the weight that he is pushing.
Players could even load large caliber weapons onto the cart to give them a semi-stable platform:
They will however have a limited arc and the player will no longer be able to hold anything in the cart until the weapons are removed.
But shopping carts are not the only option a player has:
These large cargo carts will store more items than a shopping cart, but at a cost of not being able to mount weapons. These carts could also potentially be used as a small, mobile barricade. Just simply load up cart with heavy metal plates and one could slowly move across a line of fire with relative safety, or even potentially use it as a battering ram.
The weakness of carts however comes with their low health and cover; a mobile LMG on a shopping cart sounds menacing, but players operating the cart have little to no cover and shopping carts have a perfect basket for catching grenades and other explosives.