Yes! When you add a gift from another store, you can choose to receive the cash equivalent of the gift (so you can buy it yourself) or direct guests to purchase it for you on the other store's website.
To be able to turn the gift into a “Group Gift,” make sure you select “Get cash equivalent for this gift.” Then under “Manage Registry,” click on the gift to edit it and mark it as a “Group Gift” so guests can contribute what they wish to it.
Please note: if you direct guests to the other store’s website to purchase the gift, the gift cannot be turned into a “Group Gift.”
You can learn more about how to enable “Group Gifting” here. And for more on adding gifts from other stores, visit this page.