def combine_on_sep(items, separator):
    """
    Combine each item with each other item on a `separator`.
    
    Args:
        items (list): A list or iterable that remembers order.
        separator (str): The SEPARATOR the items will be combined on.
    
    Returns:
        list: A list with all the combined items as strings.
    """
    combined_items = []
    # Combine items only if there is more than 1 items.
    if len(items) > 1:
        # Convert the empty string back to minus.
        items = [i if i!='' else '-' for i in items]
        for i, item in enumerate(items):
            reduced_items = items[:i] + items[i+1:]
            combined_with_item = [separator.join((item, r)) for r in reduced_items]
            combined_items += combined_with_item
    # Else simply return the given list.
    else:
        combined_items = items
         
    return combined_items