Oauth2 to multiple Jira accounts

We have an app built where uses go through the Oauth2 process and we can make REST calls as expected.

We have a situation where a single user may have Jira accounts in different Jira Cloud systems. We have found that once the user goes through the Oauth process, if they wish to do the oauth process and use a second Jira account they cannot.

That is, there is no opportunity in the flow for them to login to a different account. I’m assuming based on cookies saved, they get auto-authenticated and don’t need to login, Should this be possible?

I found that the only way to have them be able to login to a different Jira account is if I delete all “atlassian” cookies from the browser (I delete all, but I’m assuming only. sibset are at play)