Idea Summary
In a dynamic action, you can open a pop-up LOV for the affected elements type Item(s)

You can apply a search filter when there are many page items.
But when you need to select more than one item, the search filter is cleared on reopening the pop-up LOV for the next item. 

This takes more effort to select the required items.

Use Case
All pop-up LOVs with a search filter where you can select more than one item.

Preferred Solution (Optional)
The page item popup LOV already behaves like this.
Only the internal APEX builder is not.