At the University of Florida we have a written policy that defines who can and who can not serve as a PI on UF funded projects (see below.) 

However, it is possible for a department chair or major research center director to certify that a "non-eligible" person be made eligible (on a case- by-case basis.)  The person requesting this must justify this request in writing to the Director of Sponsored Research who will make an approval decision on the request.  Such justification might include several years of past experience managing projects of similar complexity and scope, particular expertise not available from other eligible employees, etc.  This request must also state which "eligible" faculty member will serve as a Co-PI to provide back up and continuity should the "non-eligible" person be unable to fulfill his/her duties in the role of PI.

UNIVERSITY OF FLORIDA - C & G POLICY
Eligibility to Submit a Proposal for External Funding
University Policy has established that any individual who holds one of the following positions and has signed the Patents and Copyright Agreement can be a principal investigator and submit proposals for external funding:

(a)
Faculty in Tenure Accruing Tracks
Assistant Professor, Associate Professor, Professor
Assistant Curator, Associate Curator, Curator
Assistant Librarian, Associate Librarian, Librarian
Graduate Research Professor
Distinguished Service Professor
Distinguished Research Curator
Emeritus Professor
Eminent Scholar

(b)
Faculty in Non-Tenure Accruing Tracks
Assistant Scientist, Associate Scientist, Scientist
Assistant Scholar, Associate Scholar, Scholar
Assistant Engineer, Associate Engineer, Engineer
Assistant Research Professor, Associate Research
Professor, Research Professor
Assistant Extension Scientist, Associate Extension
Scientist, Extension Scientist
Clinical Assistant Professor, Clinical Associate
Professor, Clinical Professor

(c)
Other University Faculty and Personnel
Instructor/P.K. Yonge Developmental Research School (PKY),
Assistant Professor/PKY, Associate Professor/PKY,
Professor/PKY
IFAS County Extension Faculty
Instructors

Investigators in the following categories are not eligible to submit a proposal unless they have a person in one of the above positions serve as their co-principal investigator and have approval from Research & Graduate Programs:

Lecturer
Visiting Faculty
Assistant In, Associate In
Research Associates
Courtesy Faculty
Postdoctoral Employees
OPS Faculty
Graduate Students


New Investigators must have completed their required degree and hold a university appointment at the time of application or expect to hold an appointment by the effective date of the award.
Hope this helps!