Multiple Login's on the same page

We are at the stage where we are getting ready to integrate with a potential client and the topic of how login should work came up. Currently the potential client has its own proprietary login system, we have built our tool so that you do not need to login at all, you can purchase the product without ever logging into to our system. We only require your email address so we can send you a confirmation.

This is causing a technical challenge, the potential client wants us to integrate into their login system, however we think that building links to proprietary login systems for all clients is not scalable. The other option we have is to offer the clients two login's, which we think is stupid. The challenge with that is from a UI perspective, having 2 login's on the same page seems confusing and amateur.

Any advice?