Hello @Mytoast Admin
Thank you for reaching out Microsoft Q&A.
I understand that you're trying to set up SSO with third-party apps, such as e-commerce platforms, that are used by both internal and external users across the organization, and you're asking if it's possible to configure SSO using SAML and OIDC without receiving SSO or other details from the app/service provider.
I hope Answer provided by @Marti Peig is helpful.
Additionally, you can add any application that already exists in your organization, or any third-party application from a vendor who isn't already part of the Microsoft Entra gallery. Depending on your license agreement, the following capabilities are available:
Self-service integration of any application that supports Security Assertion Markup Language (SAML) 2.0 identity providers (SP-initiated or IdP-initiated)
Self-service integration of any web application that has an HTML-based sign-in page using password-based SSO
Self-service connection of applications that use the System for Cross-Domain Identity Management (SCIM) protocol for user provisioning
Ability to add links to any application in the Office 365 app launcher or My Apps
Each of your applications might have different authentication requirements. With Microsoft Entra ID, signing certificates can be used with applications that use SAML 2.0, WS-Federation, or OpenID Connect Protocols and Password Single Sign On. For more information about application authentication types, see Managing certificates for federated single sign-on in Microsoft Entra ID and Password based single sign on.
for additional information you can follow: https://learn.microsoft.com/en-us/entra/identity/enterprise-apps/plan-an-application-integration#capabilities-for-apps-not-listed-in-the-microsoft-entra-gallery
Hope this helps. Do let us know if you have any further queries.
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Regards,
Harshitha Eligeti.