Reorder levels of MultiIndex in a pandas DataFrame

It's better to use reorder_levels to manipulate the order of MultiIndex levels. Just pass in a list of the level names/numbers in the order you want:

>>> df.reorder_levels(['Letter','Color','Number'])
                     Value
Letter Color Number       
a      Red   1          41
       Green 1          56
b      Red   1          43
       Green 1          42
c      Red   1          89
       Green 1          18
a      Red   2          55
       Green 2          93
b      Red   2          64
       Green 2           9
c      Red   2          21
       Green 2          93

There's also swaplevel if you simply want to swap the positions of two levels.

Inplace Modification

Call MultiIndex.reorder_levels, then assign the new index to your DataFrame.

df.index = df.index.reorder_levels(['Letter', 'Color', 'Number']) 
df

                     Value
Letter Color Number       
a      Red   1          41
       Green 1          56
b      Red   1          43
       Green 1          42
c      Red   1          89
       Green 1          18
a      Red   2          55
       Green 2          93
b      Red   2          64
       Green 2           9
c      Red   2          21
       Green 2          93

Since Index objects are immutable, you cannot get over creating a new Index, but you can avoid duplicating your data by otherwise calling df.reorder_levels.