It sounds like:
- you're working within an architecture that limits functional changes,
such as SSO > system direct to appropriate service;
- having two separate pages (one for each service) isn't up for
- that the user has one set of credentials that works for both
So if the question is should you allow log in for two services in one space to free up space visually, then that really depends on if freeing up space is important.
I think two separate logins (example below) on one page is a lot to handle.
Some sites treat log in and sign up in this manner. In this example, you rely on the user to parse very similar information in a quick way.
Combining the log ins into one space can make a lot of sense visually, but I might avoid a drop down.
This method isn't one I see very often anymore and somewhat complicates the process. and I prefer to keep the log in as focused as possible (tasks: choose first before entering information > only show log in fields > enter information > log in)
So, I might provide a tab/toggle structure instead:
Ultimately though, if you can move in the direction of one login, with a SSO, I would try that.
Hope this is helpful.