Yes, but only on rare occasions & for really, really good reasons.
The school you are leaving must accept you to leave (& transfer the federal money) & the school that you want to transfer to must have room, you must satisfy their admission requirements & it must be at a time at which you can transfer without losing something in the process (dependent on the curriculums of both schools).
A finace wouldn't be a reason. A spouse who is pregnant or ill would be a reason as would be an ill parent & you being the only child. But, in these cases, they might recommend a year off rather than a transfer. Married spouses live apart during school years frequently.
I've only known it to occur about once per class, if at that.