BUG: reindexing a level in MultiIndex has no effect

[attack68]

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• (optional) I have confirmed this bug exists on the master branch of pandas.

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This is about trying to reindex a MultiIndex level to add keys to avoid a KeyError.
This code could be more minimalist and more generic but the context in which the error arose might be helpful..
When using groupby unnecessary keys are eliminated..

idx = pd.IndexSlice
df = pd.DataFrame([
    ['A', 'cat', 10],
    ['A', 'cat', 20],
    ['B', 'dog', 30],
    ['B', 'cat', 40]
], columns = ['Label', 'Animal', 'Score'])
g = df.groupby(['Label', 'Animal']).agg('sum')
g.index
>>> MultiIndex([('A', 'cat'),
               ('B', 'cat'),
               ('B', 'dog')],
                names=['Label', 'Animal'])
g.loc[idx[:, 'dog'], :]     # <--- WORKS because 'dog' is an element of level 1.

But...

g = df[df['Label']=='A].groupby(['Label', 'Animal']).agg('sum')
g.index
>>> MultiIndex([('A', 'cat')],
                            names=['Label', 'Animal'])
g.loc[idx[:, 'dog'], :]     # <--- KeyError  because 'dog' is NOT an element of level 1.

I tried to solve this with

g2 = g.reindex(pd.Index(['cat', 'dog'], name='Other'), level=1)
g2.index
>>> MultiIndex([('A', 'cat')],
           names=['Label', 'Animal']).     # <-- Reindex did nothing.

The docs for Index.reindex don't mention the level argument or give any examples, the docs for DataFrame.reindex were better but still not actually consistent with the arguments and no multiindex examples. And I tried to find any relevant parts of the guide which deal with reindexing multi indexes but without success.

Now that Indexing with missing keys returns a KeyError is it more important to provide example for these issues? Or have I missed something very simple.

[attack68]

Im will close this due to more info in #39775