How can I add a level to a MultiIndex?

Question

index = [np.array(['foo', 'foo', 'qux']),
         np.array(['a', 'b', 'a'])]
data = np.random.randn(3, 2)
columns = ["X", "Y"]
df = pd.DataFrame(data, index=index, columns=columns)
df.index.names = ["Level0", "Level1"]
print df

                      X         Y
Level0 Level1                    
foo    a       0.418549  0.252685
       b      -1.307099  0.202833
qux    a       0.046095 -0.968976

New level

I want to take the index of df and create a new MultiIndex that now has an additional level.

new_level_name = "New level"
new_level_labels = ['p', 'q']
# new_multi-index 

Desired MultiIndex

Level0 Level1 Level2                    
foo    a      p       
              q       
       b      p      
              q       
qux    a      p      
              q      

Answer 1

The simpliest is use stack with new DataFrame with columns by new level values:

df1 = pd.DataFrame(data=1,index=df.index, columns=new_level_labels).stack()
df1.index.names = ['Level0','Level1',new_level_name]
print (df1)
Level0  Level1  New level
foo     a       p            1
                q            1
        b       p            1
                q            1
qux     a       p            1
                q            1
dtype: int64

print (df1.index)
MultiIndex(levels=[['foo', 'qux'], ['a', 'b'], ['p', 'q']],
           labels=[[0, 0, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0], [0, 1, 0, 1, 0, 1]],
           names=['Level0', 'Level1', 'New level'])