I use Shopify Buy Button and it seems at the moment, even when I add multiple products on the landing page, when people click on the buy button, they are brought to check out process immediately, without being able to add other products. Can Unbounce make this happen?
You need the button to link to your Shopify Store, not the cart. Then control the store through one of the Shopify themes.
Most probably, you have your buttons linked to the “Checkout” instead of the “Cart” option as Jason mentioned.
Here is the documentation from Shopify related to it.
Another great resource, I’ve referred a few times when working with Shopify is this blog post that has a few examples of external embedding.
However, you should ideally have a single product per page. It would allow you to better target your traffic and make the whole landing page relevant to your intended audience/product. If the other products on the page are complimentary, you can try some of the upsell/cross-sell apps for Shopify.