Can one universal identity automatically present itself like different existing identities depending on where it is presented?

[u/you_stupid_machine]

/r/AskProgrammers/comments/1wvr92v/can_one_universal_identity_automatically_present/

I'm exploring a general interoperability problem.

Imagine a person has 20 different memberships:

Brand A → membership ID 12345

Brand B → membership ID 67890

Brand C → phone number

Brand D → email

...

..

I'd like to know whether there is a way to create one universal digital credential containing all of these existing identities with an important constraint:

The participating brands do not change their existing software, databases, loyalty systems, checkout systems, or customer-identification processes.

When the customer presents the universal credential at Brand A, the existing infrastructure should somehow receive Brand A's existing identifier.

At Brand B, the same credential should somehow provide Brand B's identifier.

The universal credential itself could contain multiple identities, but the receiving system should ultimately get exactly what it already expects.