Technically, you can with most agencies for the recreational courses but it is different for professional levels. Also, some instructors from one agency my require an "upgrade" training when a student coming in from a different agency/instructor for more advanced courses as I do myself. When a potential student comes to me for the Advanced Scuba diver or higher who did their prior training with a different agency/instructor, I always require two extra pool sessions, one or two in class sessions and one openwater session in addition to the respective course training. I don't take anyone from other agency/instructor without evaluation and remedial work straight into my upper level courses. They pay extra for the course.
