with a search filter that allows to narrow down the search using 3 different taxonomies. Now, when the user selects more than one value within the same taxonomy or chooses 2 different taxonomies, the results are broadened, while I need it to be the other way round: it should be an "OR" instead of "AND".
Just to clarify what Minesh wrote, it is possible to modify the query to specify 'AND' instead of the default 'OR' using the pre_get_posts hook when it comes to applying filters for terms from different taxonomies (e.g. only show posts that have this colour AND that size), but it is not possible to modify the behaviour when filtering by terms from the same taxonomy (e.g. if you choose 'red' and 'blue' terms of a colour taxonomy, that will always be interpreted as show posts that are either red or blue).
That relates to how taxonomy queries behave in WordPress, it is not specific to Toolset. It may be possible to modify this behaviour by creating custom database queries, but that is outside the scope of support we can give, I'm afraid.
