Web Application: Clear Cached Credentials from NTLM Challenge when failed attempt

Question

We have a web application that users would normally use a logon SSO page to get into. When users provide the wrong credential (a valid credential, but not one that has access to the application) their credential is cached and they can no longer provide a different username/password.

So far the users are using incognito (private browsing session) to bypass this if this mistake happens.

However, we would like to have our application clear the cached credentials if the logon attempt is successful but the user lacks permissions.

We can't seem to figure out if this is even at all possible. We can only influence the client side SSO page, as the web application we use is proprietary and we do not have access to the backend/server-side code.