There's nothing stopping you from thinking about it after the deadline, but if you want any corrections to be graded, you need to tell the professor before the deadline. It's possible he'll give you an extension, especially if you have good reasons (e.g. personal issues).
Handing in assignments after the deadline, without warning, is likely to lead to it simply not being graded. The professor must be fair to other students who might not have had the extra time, and besides, if he accepted your submission everyone else might start doing the same and the deadline might as well not be a deadline.