Is there an easy way to move an object from one class or layer to another?

CAN YOU MOVE A DRAWING THAT IS COMPOSED OF MULTIPLE LINES AND OBJECTS TO ANOTHER LAYER? DO YOU HAVE TO DO IT ONE OBJECT AT A TIME? 

my design layer is vanishing when I activate another design layer. I have the layer option set to show/snap others. all the classes are active! 

what am I missing. 

@JANE H. If you have both the class and layer options set to at least Show/Snap Others, all classes active, and both design layers active, then objects from both design layers should show up. If that is not the case, you might check your design layer scales; only design layers using the same scale will show up.

Tools>Organization. Design Layers tab. Edit Scale for each layer if needed.

Perhaps also check you have unified view activated.