There is only one designcenter, but yes you can copy blocks from one DWG to another DWG.
Only the receiving DWG needs to be open, but you can have both open.
If you have two dwgs open you can copy things from one dwg to the other thru both design centers. In fact looking for thie block thing i found you can copy layers, linetypes, dimstyles. almost everything. Love this program. Learn something new everyday.
The block i was wanting to copy is assigned to a point and i will need to figure out how to do that. That is a different story than just inserting a block.
But to repeat, there is only one "designcenter". It's a palette, it doesn't belong to a drawing.
So you can have 20 drawings open and there will only be one designcenter.
And only the receiving drawing has to be open