Would it be possible to add a search box to the so-called second level.

If I choose a cell "Make / Model", such as the BMW, then the next box should be:
---------------
1 Series (all)
116
118
120
123
and so on...
2 Series (all)
...
---------------

By default, it shows
---------------
1 Series (all)
2 Series (all)
...
---------------