Julie here from Shopify Support.
When dropshipping, working with multiple suppliers can definitely add complexity to your business. If one of your customers places an order for several products that come from multiple suppliers, the items will need to be shipped in separate packages. This is because each supplier is completely independent and they likely have different warehouses and distribution centres. Unfortunately, there isn't any way around this and this is simply a reality of dropshipping with multiple suppliers.
For this reason, it's ideal to try and find a single supplier that provides all your products. Similarly, you could choose suppliers that carry very different types of products that would be less likely to be combined in the same order. This could help reduce any instances of customers ordering multiple products from different suppliers.
Another option would be to acquire your own inventory and ship products yourself. If you contact your suppliers directly, they may even be able to offer you a bulk discount. While this method would require you to invest more capital into your business, it would give you more control over the fulfillment process. It's also likely that your customers would receive their orders faster, as you'll be able to ship domestically. If you're located in the United States, Canada, or Australia, you could even use Shopify Shipping to purchase and print discounted shipping labels from carriers like UPS, USPS, DHL Express, Canada Post, and Sendle.
Aside from the above options, I also recommend checking out this forum post, which sheds more light on these situations and offers some potential workarounds.
All this being said, it’s unlikely that your customers will mind receiving multiple packages for a single order – some of the largest ecommerce businesses in the world also ship packages this way. If a customer does complain about this, you can let them know that your distribution centres are located worldwide, so this is the fastest way to deliver their products. Oberlo actually has a help doc on how to communicate with your customers about shipping here. This help doc will show you how to edit the shipping confirmation email template that customers receive, and how you can also email customers manually through Shopify/
As you continue working on your dropshipping business, I suggest checking out Oberlo's blog post, "21 Days to Your First Dropshipping Sale". There are a ton of great tips in there to help you start boosting traffic and generating sales. I think you'll find it quite useful!
Have you already launched your store? What kind of products are you selling?