Authenticate one node backend in two private Keycloak clients on the same realm

Question

I have two APIs, each of which have a Keycloak client in the same realm. I want to connect a node backend (in the context of a backend-for-frontend architecture) to both APIs at the same time.

At the moment it connects only to one, I'm using openid-client. Is there a way to log in to both clients at the same time?

As far as I understand, once a user logs in they have a session in the Keycloak realm. With public clients, when I send the users to log in to a second client it does not request the users to input again their credentials, just returns a new token with the updated credentials. But in this case is not a public client, and I don't have a default client to which I want to log in first: when a user comes in to the app I don't know if they have access to either one of the APIs or both, so I would like to attempt to log them in for both clients from the start.