Replace singular value on second level of pandas dataframe multiindex when that index level has identical values

I have a dataframe that has a multiindex with two levels. Given the following example for the second level:

d = {
"col1": [1, 2, 3, 4],
"col2": [1, 2, 3, 4],
"col3": [1, 2, 3, 4],
"col4": [1, 2, 3, 4],
"col5": [1, 2, 3, 4],
}
df = pd.DataFrame(data=d)
df.columns = pd.MultiIndex.from_product([df.columns, ["identical"]])

How do I change a singular value so that the second level of the index looks like this?

['example', 'identical', 'identical', 'identical', 'identical']

I have tried to do it this way:

        updated_columns = list(df.columns.get_level_values(1))

        updated_columns[0] = 'example'

        df.columns.set_levels(
            updated_columns, level=1, inplace=True, verify_integrity=False
        )

My change is ignored in this case.

I have also tried the answer from this topic: pandas MultiIndex with duplicate values in one level

        df.columns = pd.MultiIndex.from_tuples(
            df.columns.set_levels(updated_columns, 1, verify_integrity=False).values
        )

Which was also ignored.

I have also considered using the rename() method. Unfortunately it only works if the value of the column that is renamed is provided. Given that there are identical values, this will not work.

For non-multiindexes there is this method:

df.columns.values[0] = 'example'

But from what I have gathered, it will not work for a multi index.

I have added verify_integrity=False because the method would not otherwise allow me to set identical values.

Any help would be appreciated.

>Solution :

One way would be to get the tuples that make up the MultiIndex and modify them directly:

tuples = df.columns.tolist()
tuples[0] = (tuples[0][0], 'example')

df.columns = pd.MultiIndex.from_tuples(tuples)

Output:

>>> df
     col1      col2      col3      col4      col5
  example identical identical identical identical
0       1         1         1         1         1
1       2         2         2         2         2
2       3         3         3         3         3
3       4         4         4         4         4