Jumping in late, but I think the original question was more can you put players on other scholarships and still play sport X. That answer is no.,you can't move a guy to the track team, or give him an academic scholarship and still play football or basketball.
Maybe I misunderstood, but my thoughts on the question.
I read it to only ask about non-athletic scholarships.
You can absolutely transfer a guy from one sport to another, you just have to follow the hierarchy of sports set out by the NCAA (again, bylaw 15). Happens all the time. If a guy on the track team makes the football team, his scholarship needs to become a full football scholarship instead of a partial track scholarship.
You can easily move a guy from an athletic scholarship to an non-athletic one if he stops playing. That is what the whole "4 year deal" is about - guarantees players a non-athletic scholarship if they get hurt and have to quit the team.
It is a lot trickier to move someone from an athletic scholarship to a non-athletic one and retain eligibility. But it can be technically done. It is rarely a good option for the player.