In theory, yes. But then again, anything is possible 'in theory'. Mr. Penguin explained it well enough in no. 11 .
But I will add with this: Why would you want or need to ?
This is a philosophical question. A long time ago in a US state far far away from where I am now, I had a senior Raytheon radar engineer for a mentor and this guy was big into the philosophical foundations of everything we do. He taught me how to think backwards -- forensically.
So for your question, we would have to ask 'Why would you want or need to ?' or better yet 'Why should you ?'
If you designed something to do X, there has to be a reason why you did it that way. Why you do something is motivated by your goal, situation, predicament, environment, resources, time, and consequence. The more you critically analyze each item and how it relate to the others, the more assured you will be of your final decision and that you made the appropriate decision.
Prior to missile release, a decision must have already been made about the target and the decision maker is the human. The human basically said: 'I want this thing destroyed.' So now the next question is: 'Should you allow any deviation from this decision ?'
If you answer to yourself 'No', then you will design your missile to be without the capability to change its target focus. Your missile will be simpler in design and manufacturing.
If you answer 'Yes', meaning you want to the option of deviation, now your missile must have more fuel because there is no way for you to know when you will need redirection. More fuel means the missile will be physically larger which may affect carriage, as in you may have to carry on the wing instead of fuselage.
Maybe you want a 'point of no return', meaning after launch and the missile is on the way, once the missile reached a certain distance threshold from the target, no deviation is allowed. So now you must design in interlock switches. For example, one interlock would be calculating the distance between launch point and target, then you must design a calculated halfway point of that distance where no re-targeting command is allowed.
As you can infer, a deviation or re-targeting allowance opened a can of technical worms making the missile more complex in many ways. The return on investment (ROI) is simply not there. So while it technically feasible to do so, it is not practical to do so.