How to simply add a column level to a pandas dataframe

Another way for MultiIndex (appanding 'E'):

df.columns = pd.MultiIndex.from_tuples(map(lambda x: (x[0], 'E', x[1]), df.columns))

   A  B
   E  E
   C  D
a  0  0
b  1  1
c  2  2
d  3  3
e  4  4

As suggested by @StevenG himself, a better answer:

df.columns = pd.MultiIndex.from_product([df.columns, ['C']])

print(df)
#    A  B
#    C  C
# a  0  0
# b  1  1
# c  2  2
# d  3  3
# e  4  4

A solution which adds a name to the new level and is easier on the eyes than other answers already presented:

df['newlevel'] = 'C'
df = df.set_index('newlevel', append=True).unstack('newlevel')

print(df)
#           A  B
# newlevel  C  C
# a         0  0
# b         1  1
# c         2  2
# d         3  3
# e         4  4

option 1
set_index and T

df.T.set_index(np.repeat('C', df.shape[1]), append=True).T

option 2
pd.concat, keys, and swaplevel

pd.concat([df], axis=1, keys=['C']).swaplevel(0, 1, 1)