Yes you can. As a reminder, we are able to authenticate to your APIs via many different authentication systems (Bearer Token, API Key, Basic Auth, OAuth 2.0).
But in the case of a custom authentication solution that you would like your customers to use, you can use your own API authentication flow. At the time you connect your API on Blobr, you can select a custom option and detail your own authentication flow. This means that your users will have to follow your authentication process and add the Blobr API Key on top of your existing authentication flow.