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if the body voltage is varing that will cause a unstability in the effective threshold voltage of the device which could even effect the region of operation of your device.
if w and l are also varing then the current driving capability of the device will be effected and every time the effective drops at drain and terminal will keep on changing.
something you are suggesting is varying in 3 variables and hence has to be analysed with partial differential equations and it would vary with different extent in different regions....
If you vary the parameter W and L you change the current passed in the active region, if you change the body voltage you change the transconductance of the device and, if you are using it as amplifier, you change the gain and you can change its state of operation, e.g you can get a MOS off if the body voltage is too high and makes the Vt value goes over the Vgs voltage.
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