Kerberos 401 authentication with form fallback

That's just it. There are a number of options here. JoeTheFifth is talking about computer checks - the computer or mobile device identifies itself, and you use that information to decide whether or not to challenge the user. And that *usually* gets tracked as an IP address in a table.

If you can't manage the client devices though, the easiest option is to divide users by subnet. Authenticate-able users on one subnet, contractors and customers on another... That would be the simplest solution.

It's also possible to do "step-up" auth options. Gov customers will often do this. Bring all users to a non-auth landing page and let them choose how to authenticate - AD, client cert, user/pass. Whatever they click on triggers a secondary step-up mechanism. It's not transparent to the user of course, but a reasonable solution nonetheless.