Can Students Switch Houses?

[Robert Jones]

No: HPFGUIDX 90095

I'm still thinking about the question of which house James, Sirius, 
and Remus were in, and here's something that might complicate the 
problem further.  In PS/SS, in the night after Harry is sorted, he 
has a dream about Quirrell' turban telling him he must switch to 
Slytherin immediately.  Well, can the students switch like that?  
Didn't the Sorting Hat say he never made a mistake?  But if students 
can switch, James or Sirius or Remus might have started in one House 
and ended up in later years in another.