Showing in-stock and backorder products only

Excluding out of stock, but including instock and onbackorder products

• Open up the Frontend search settings -> Custom fields panel

• Click to create a New filter

• For the filter name you can choose anything, we typed "Stock"

• For the field name choose _stock_status

• For the field type choose Hidden

• For the field value enter: instock::onbackorder

• For the field operator choose EXACTLY LIKE

• Save the field and the search settings