This mod adds a new item to the game: Chest Transporter. This item allows you pick up a chest with its items and place it somewhere else. You can also pick up chests from a storage minecart and place it in a normal minecart. But while you have a chest in your inventory, you dig and walk slowlier, have more hunger and can not jump over one block.
https://www.curseforge.com/minecraft/mc-mods/chest-transporter