Extend A DataGridView ComboBox Column's Edit Control By A Second Tiny Button?

I insert DataGridViewComboBoxColumn columns in a DataViewGrid. That works fine.

Now, I want the user to be able to not only select one list item, but to "drilldown" into the list that is behind the combobox, allowing him to edit (insert/delete/update) the list.

I think it would be a good idea to display a ".." button right behind the dropdown button of the combobox. Pushing it leads to a dialog where the list can be maintained.

What I am stumbling upon is:

How would I create such a custom combobox? Is ComboBox (which is the base for the combo box that the combo box column creates as its edit control) open enough to accommodate such an additional button? What would be the container of the tiny buttoon -- the ComboBox descendant? How I would make the grid create and handle such a custom combobox?

I currently try to solve this by subclassing DataGridViewComboBoxColum, using a DataGridViewComboBoxCell descendent in its CellTemplate assignment, and overriding PositionWEditingPanel and PositionEditingControl to manipulate the sizes of the panel and the combobox so I'd have space for the tiny button. Is that the correct way?

Or would I have to create a DataGridViewColumn descendant which creates a Panel containing a DataGridView combobox edit control and the tiny button? How would I make sure the column keeps care of the combo box so it has the correct items etc?