Quick Answer
Yes, you can add schools after taking CASPer, but only if two things are still true: the program is accepting score distributions for that admissions cycle, and the program requires the same CASPer test type you already took.
That second condition matters. CASPer is not one universal score that automatically fits every health profession, country, or language requirement. If a newly added program uses a different test type, your completed test may not satisfy that requirement.
If your score has already finished the usual processing period, an eligible new distribution is usually sent within 1 business day. If your score is still being processed, the added program should receive it when results are released to your distribution list.
For the broader CASPer timeline, start with the Ultimate Guide to CASPer. This page focuses only on post-test school additions.