This is already possible using the search filters. For example, a link to identify plants in the genus Fumaria, but excluding those already identified as Fumaria capreolata or Fumaria officinalis: https://www.inaturalist.org/observations/identify?taxon_id=53787&without_taxon_id=57852,53785
There is an open request to add this capability to the user interface, rather than requiring manually editing the URLs. You can vote on that here: https://forum.inaturalist.org/t/exclude-certain-taxa-in-identify-user-interface/3232