Yes you can have more than one of the new staff at the same time. I was able to hire both the Psychologist and Nutritionist and both are showing up on my staff page now.
The reason I'm asking is that I can't find nowhere the button "Hire" that you have without the new staff.
I only see this find replacement button, and we know what replace means, to bring a new one instead of the old staff member...
(http://pokit.org/get/img/3295364e7ff2a661790ee815c75f7ecf...)There should be definitely a "Hire" at the bottom of the page for the new Secondary Staff.
This is where we hold them!