Steam will not allow you to activate a key for a game that you already own, even if the key you're attempting to activate includes additional inventory games for you to gift.
To work around this you can either:
- Create a new Steam account, log into that new Steam account, activate the multi-pack key in this new account and gift the items from the new account's inventory.
Note though that this option WILL assign one of the multi-pack games to the new Steam account in which you activate the key.
- Send the key to one of the other Steam users that you want to gift the game to and who you trust for them to activate and gift the additional copies on as you ask them to.