Can you move some else’s Jenga piece?
If the block was properly placed

That's not legal.

It's not legal to move a block from an incomplete top row. 

It's not legal to move a block from the topmost complete row. 

In fact, if you start moving a block other than the one you move to the top, you must put it back into its original position before continuing.


  You can touch other blocks to find a loose one &mdash; but if you move a block out of place, you must fix it (using one hand only) before touching another block.




If the block wasn't properly placed

Although not stated in the underspecified rules, it's the responsibility of the player placing the block to place the block on the top layer according to the same pattern used during setup.