Make third-party cookie become first-party cookie

We have a Drupal website embedded to other websites.
For example, the websites can embed our website in their website as following:
<iframe src="drupal_site_url"></iframe>

In this situation, Drupal site cookie becomes third-party cookie.

Now more people block third-party cookie, so our Drupal site can not function inside
the other websites this way.

We have a control for the websites which embed our Drupal site.
For example, we can modify the way like JavaScript, iframe.... to embed the Drupal site.
Is there a method to make our Drupal site cookie become first-party cookie?
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Ray PaseurCommented:
I don't think so.  A better design would be to have your "drupal_site_url" turned into a "drupal_site_api" so that you can produce a consistent and versioned API response to the request.  Then web sites that want your content can access the API via cURL or similar and get the information in a way that doesn't trigger security alerts.  You might want to consider publishing via JSON.

Information on APIs:

Information on HTTP client/server protocols:

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