How to add custom status to quick edit

Unfortunately there are no filters or actions for modifying the post status select in quick edit (WP_Posts_List_Table::inline_edit()) – you’d need to resort to JavaScript:

(function($){
    $( "select[name=_status]" ).each(
        function () {
            var value = $( this ).val();
            if ( value === "pending" )
                $( "option[value=pending]", this ).after( "<option value="status-1">Status 1</option>" );
            else if ( value === "status-1" )
                $( "option[value=status-1]", this ).after( "<option value="status-2">Status 2</option>" );

        }
    );
})(jQuery);