drop down category search

There are other similar posts but not quite what I am after…

I would like to have 3 drop down menus on my homepage, that show all of the categories used in the site. The visitor could select a different category in each drop down, and then press a search/submit button. This would return all posts that appear in all 3 selected categories.

I have tried the Multiple Category Search Widget but it does not really do this.

This doesn’t seem too ambitious for a database driven system – is there a way to achieve it?

Thanks
S