Would each of Walmart's vendors have their own IdP?
Assuming so, your SAML configuration for Walmart would have multiple partner identity providers (eg one each of Walmart, trucking company A, trucking company B, security company).
You would still use the "walmart" subdomain name as the configuration ID when loading the SAML configuration.
SAMLController.ConfigurationID = "walmart";
When you call SAMLServiceProvider.ReceiveSSO, our API determines which partner identity provider within the Walmart SAML configuration sent the SAML response and process it accordingly.