Is it possible to setup openid without well-know configuration?

you can have oauth2_client_credentials or oauth2_introspection in oathkeeper (other proxies are also capable e.g. nginx)

Sorry, I meant as in openid connect authentication method. For example I mean manually setting the endpoint URLs and not using the well-known configuration JSON at all.

yeah it's possible take a look at here: https://www.ory.sh/docs/oathkeeper/pipeline/authn

I mean in Kratos

In kratos there is a configuration (source) that can specify the oauth2_provider though, honestly I haven't tried also, you mentioned that you wanted a hosted version and it seems like the Ory Network doesn't provide the hosted version of Oathkeeper that said, perhaps your best next option is to host just the oathkeeper and configure it to talk to the hosted kratos

So I think the provider URL you configure and it will then look at the .well-known JSON file from that URL. THe problem is the LINE openid connect configuration JSON is misconfigured, so I want to override that