Hello Frippery -
The MultiChannel service has two options for inventory and you can select which you wish to use in your Account Preferences.
If you use Allocated Quantity, you are setting an inventory level per channel for a given product and will need to update that per channel when you need to add further inventory.
There is also the option to Auto Sync Quantity, so you have a pool in your inventory for a given product that updates as sales occur across various channels.
If you are experiencing issues or have more specific questions regarding your inventory, please feel free to file a support case using the Help options for your account so we can have a look into it.
- Craig