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The conventional place to hold the racket is with about one centimetre away from the bottom of the butt. Some people hold the racket further up which they feel gives them more control. The lever between the ball on the strings and the racket hand is shorter which makes the racket head feel slightly lighter and provides more control over the maneuverability of the racket head.
Other players prefer to hold it right at the bottom which conversely give you a longer lever and allows you to swing the racket head slightly faster but it is harder to control. Hence you have more available power.
It is possible to move your grip mid rally between shots although this is quite a difficult skill to master. It may be better to hold the racket further up or down depending on how it suits your game.