Question for Harry Potter fans?

This question looks simple when written but any serious Harry Potter fan might know how Hogwarts works and so in truth it may be more complicated: We all know that the Sorting Hat puts every first year student into a specific House. But after, say, several months to a year at minimum, if Severus Snape wanted a certain Gryffindor student (and this "certain Gryffindor student" refers to any of them, not just "Mr. Coincidence" Harry Potter) in Slytherin, so he could keep a better eye on the student, could he speak to Minerva McGonagall and Albus Dumbledore and ask Dumbledore to authorize the switch? (If you must know why I'm asking this question, it's for a unique type of fan fiction involving a VERY young first-year Hogwarts student - it goes that, she likes Snape and Snape likes her, and by the end of her first year Snape wants her out of Gryffindor and in Slytherin for the rest of her years there. The girl, who is actually seven at the start of her first year and was admitted early due to an awesome knack for witchcraft, is a pure-blood, by the way). Thanks in advance for your help, guys!