Can you use a datagrid instead? Datagrids natively support multiselection so you can have your two filtered grids, with a button that runs a microflow to update your selected objects in such a way that they no longer show in the first grid, but they show in the second.

If you need to use listviews, then I’d suggest using a Helper entity: create a new non persistent entity with a reference set to the entity you need to move from list to list. On your page, have a dataview of your new Helper entity, and inside, show your two lists. each time you select an item from list A, run a nanoflow to add that object to the reference set of your helper object. Then, a button can run and move all the associated items over to the other list.