Are school transfer and course shifting allowed under the SSS Educational Assistance Loan Program?

Yes, these are allowed.
But you can continue to borrow only for the remaining years of the course you applied for in your initial application.

In your initial loan application, you wrote that your course is a 4-year course, and before you shifted, you already have borrowed for 1 year or for 2 semesters.
You shifted to a 5-year course.
SSS says that you can borrow only up to 3 years, since that's the remaining number of years for you to finish your initial course, as written in your initial application.

This means that if you started at first year in your new course, you can no longer apply for a Subsequent Loan in your 4th and 5th years.

 Circular 2014-002
signed Februry 11, 2014

Subject: Addendum to the Terms and Conditions of the SSS Educational Assistance Loan Program

D. Miscellaneous Provisions

   1. The processing of subsequent applications whose beneficiaries were retained in the same year/program level or have shifted course or have transferred to another school shall be allowed, provided, the subsequent loans shall be approved up to the extent of the remaining number of releases based on the approved initial educational loan.

Any unused allocation upon course completion shall be returned to the available EALP fund for allocation to the wait-listed new/initial educational loan borrowers.

The number of maximum releases shall follow the standard number of semester/trimesters/quarters terms per course regularly offered by schools.

NOTE:  The SSS Educational Loan Program is still suspended as of June 2014. All remaining funds have been allocated for Subsequent Loan applicants. Only Subsequent Loan applicants are being approved.