A global shortcut like Ctrl + Shift + "/" (without the need for pre-selected text) brings up the search frame with a drop down of diff sites & a searchbox. It can be docked at the top of the window in the grid view for a group. 

search frame:

+-------------------------------------+
| [   site   [v]]:  [    ?words?    ] |
+-------------------------------------+

dropdown:

  [   site   [v]]
  |-------------|
  | site 1      |
  | ...         |
  | ...         |
  |-------------|
  |Groups:      |
  | group 1     |
  | ...         |
  +-------------+


definition frame attached to the search frame:

+-------------------------------------+
| [   site   [v]]:  [    ?words?    ] | 
+-------------------------------------+
|                                     |
|                                     |
|              definition             |
|                                     |
|                                     |
+-------------------------------------+

Advantages:

* allows you to carry out another search directly
* "      "   "  look up the same/diff word on another site
* reduces the dependence on keyboard shortcuts