from collections import defaultdict

def group_nested_dict_by_common_value(nested_dict, nest_key):
    result_dict = defaultdict(list)
    for key, val in nested_dict.items():
        result_dict[val[nest_key]].append((key, val))
    return dict(result_dict)


# 示例用法
nested_dict = {
    'a': {'b': 1, 'c': 2}, 
    'd': {'b': 3, 'c': 2}, 
    'e': {'b': 1, 'c': 4}
}
nest_key = 'c'

result = group_nested_dict_by_common_value(nested_dict, nest_key)
print(result)
# {'2': [('a', {'b': 1, 'c': 2}), ('d', {'b': 3, 'c': 2})], '4': [('e', {'b': 1, 'c': 4})]}