I like the philosophical angle.
I will add some additional thoughts...and
@Starlord
Every missile have the capability to re-target.
https://en.wikipedia.org/wiki/Infrared_homing
Early infrared homing missile often were misled by the sun. This is the clue that every missile
MUST be able to re-target.
Whatever the sensor -- radar, IR, or camera -- we cannot guarantee that the sensor will have %100 target view from launch to impact or near proximity.
So it begs the question of: What do we do in the event that the sensor lost sight of the target, whether that sight is radar, IR, or camera ? We incorporate a re-targeting process.
Take infrared, for example...
At its basic idea, IR is about contrasts (plural) of infrared radiation between multiple bodies or sources.
http://coolcosmos.ipac.caltech.edu/image_galleries/ir_zoo/images/apeside_ir.jpg
For the above example, only humans recognize that the cluster of IR sources resembles that of an ape, but for the IR sensor and its processes, the sensor sees only contrasting IR sources.
For the IR homing missile, we design the system so that it is attracted to the highest intensity IR source among sources. If somehow the sensor lost that contrast and somehow that contrast reoccurred, we design the system to re-acquire that highest IR source. Unfortunately, for the early IR homing missile, the sun simply overwhelmed any other IR sources, so that re-targeting process steered the missile towards the highest intensity source -- the sun.
Same idea for chaff against radar homing missile. The chaff cloud creates the highest intensity of reflected radar signals so the missile's re-targeting process steered the missile towards the chaff cloud. Only humans sees the chaff cloud. For the missile's radar, it sees a large voltage spike.
The human brain is equally vulnerable to the re-targeting process. We say that the human vision is attracted the motion, but that is not true. It is our brain that is 'wired' to be attracted to motion. That is why a truck being larger will attract our attention more than a car. We have just performed that re-targeting process.
The original question seemed to be about if it is possible for a SAM to re-target via an outside command ? The issue is not about engineering because of course we can. But now, in addition to the missile being aware of its target, there must be another observer of the entire battlefield, readied to make quick judgement and command the missile to perform that re-targeting process. That observer can be a guy on the ground with a binoc or a team of radar operators in an AWACS. From this point on, the missile's sophistication and technical complexity increases, as well as the financial burden to build it.
To date, we have opted to let the missile make its own re-targeting decisions based upon the programming that we give it. The result is the great differences in performance among competing arms manufacturers. One company may know how to distinguish chaff from aircraft while the competing company do not. This is about warfare, so manufacturers do not give guarantees.