title: Pandas adding two Multiindex Dataframes
body: <p>I'm trying to add two dataframes with Multiindex Columns and different index sizes together. What is the most elegant solution. And example is:</p>
  
  <pre><code>names = ['Level 0', 'Level 1']
  cols1 = pd.MultiIndex.from_arrays([['A', 'A', 'B'],['A1', 'A2', 'B1']], names = names)
  cols2 = pd.MultiIndex.from_arrays([['A', 'A', 'B'],['A1', 'A3', 'B1']], names = names)
  df1 = pd.DataFrame(np.random.randn(1, 3), index=range(1), columns=cols1)
  df2 = pd.DataFrame(np.random.randn(5, 3), index=range(5), columns=cols2)
  print(df1)
  print(df2)
  
  Level 0         A                   B
  Level 1        A1        A2        B1 
  0       -0.116975 -0.391591  0.446029
  
  Level 0         A                   B
  Level 1        A1        A3        B1
  0        1.179689  0.693096 -0.102621
  1       -0.913441  0.187332  1.465217
  2       -0.089724 -1.907706 -0.963699
  3        0.203217 -1.233399  0.006726
  4        0.218911 -0.027446  0.982764
  </code></pre>
  
  <p>Now I try to add df1 to df2 with the logic that missing columns are just added and that the index 0 of df1 is added to all indices in df2.</p>
  
  <p>So I would expect with the above numbers:</p>
  
  <pre><code>  Level 0          A                                   B
    Level 1         A1           A2          A3         B1
    0         1.062714    -0.391591    0.693096   0.343408
    1        -1.030416    -0.391591    0.187332   1.911246 
    2        -0.206699    -0.391591   -1.907706   -0.51767
    3         0.086242    -0.391591   -1.233399   0.452755
    4         0.101936    -0.391591   -0.027446   1.428793
  </code></pre>
  
  <p>What is the most speed and memory efficient solution? Any help appreciated.</p>