is it possible to get the MAX of a column and update it with a single query?

is it possible to get the MAX of a column and update it with a single query?

I have a scenario were i need to find the maximum value of the column and
then to update a row by increment one with the maximum value found. Can it
be done this way?
update student SET stud_rank=MAX(stud_rank)+1 where stud_id=6