Passes of the same type (e.g. coupon) and signed with the same Pass Certificate will stack up as opposed to appearing as separate. This is a feature of Apple Passbook and not controlled by PassKit. You can experiment using our PassKit Pass Certificates in the Pass settings tab of the Pass Designer.
When you issue your own Passes simply create another Pass Certificate following these instructions. You could call one Pass certificate pass.com.mydomain.description1 and the other pass.com.mydomian.description2 and so on. And then make sure you create each Pass (of the same type) using different certificates. This is especially important if your company owns multiple brands as you do want each Pass to stand alone and not be bunched up.