Does the Supreme have any wish/desire?

The Supreme who is complete by definition will have no desire or wish.
Desire or wish arises from incomopleteness. If there is completeness, there is no scope for a wish or desire to arise for seeking completeness. The Supreme has every thing in Him and never feels inadequate. Without any inadequacy, the Supreme has no need to wish or desire.
The Supreme who is complete has everything: He contains everything in the Creation and is in existence in each and everything in the Creation. All wishes and desires of everything/ everyone are contained in Him and He exists in all wishes and desires possible in all creatures. So the Supreme does not need any desire or wish of his own.
That His Creation functions the way it has been doing and will continue fully satisfies him.
With nothing remaining to be satisfied, the Supreme has no scope for any wish or desire of His own. Any thing / any one even a little less than Supreme and less than Complete can only have a wish or desire.
To put it differently, all that happens in this creation is nothing but his wish and desire getting fulfilled.