From version 3.9.7 multiselect feature will be returned to NextDBGrid, and I like to introduce you with this feature.
Same as in NextGrid, property Selected[RowIndex] specify if row is selected.
for i := 0 to NextDBGrid1.RowCount - 1 do
if NextDBGrid1.Selected[i] then ListBox1.Items.Add(NextDBGrid1.Cells[0, i]);
You may spot that approach is slightly different from multiselect in standard TDBGrid (with using TBookmarks list), but I hope that this one is better.
If you have any comments, please post it.