Can courses I took from a previous institution or UP campus unit count towards my ASIT degree?

It depends. The only way to know is to apply for Transfer of Credits. Even if you transferred from another UP campus unit or have units from another UP campus unit, you must apply for a Transfer of Credits.

Please note that you can only apply for a Transfer of Credit once you have been admitted to the ASIT program and you can only do it once. Hence, once you are admitted, please initiate the application as soon as you are able to. See How do I apply for a transfer of credit? for more details.

I am a previous BAMS student; do I need to apply for TOC to have my BAMS courses credited toward my ASIT degree?

No, you do not. Transfers of Credit are only required for courses taken outside of UPOU. As long as your BAMS courses are part of the ASIT curriculum, these will be credited.