Search multiple tags

I have been searching for a plugin that enables searching for multiple tags. I can't seem to find it anywhere.

This would be great for sites with recipes, movies, books etc.
Personally i would use it to enable searching for ingredients from recipes.

I am not looking for a search field where you type in the words, but a feature where you pick from the tags shown in the tag cloud (or a combination like supercook, see link below)

I would like the feature to show tags and then let users pick tags, show results and then maybe add further tags or remove tags to the selection.

The problem with the already existing plugins is that they only show post that have all the tags you have chosen.
The more tags you chose, the less results of posts you get from the search.
I would like it to go the other way around.
The more tags you pick out the more posts is shown in the results.
An example for this feature is:

Thank you in advance