And a number of such efforts are underway. For example, eight tonnes of liquid xenon beneath a mountain in Italy or the DAMA/LIBRA experiment discussed here on 2022-06-03.
Here are summaries of experiments for:
In addition, collisions at the Large Hadron Collider are analysed for evidence of missing mass or momentum which would be the signature for the creation of a dark matter particle which escaped without triggering the detectors. Here is a paper on “Dark Matter Searches at Colliders”.