Having two data frames with the multi-level indices in one present as columns in the other, the idea is to select those rows from the first where the index values are the same as the corresponding column values.
Example
Having the following two data frames df1 and df2:
df1 = pd.DataFrame({'i1': ['a1', 'a2', 'a3'], 'i2': ['b1', 'b2', 'b3'], 'c': [1, 2, 3]})
df1 = df1.set_index(['i1', 'i2'])
c
i1 i2
a1 b1 1
a2 b2 2
a3 b3 3
df2 = pd.DataFrame({'i1': ['a1', 'a3'], 'i2': ['b1', 'b3']})
i1 i2
0 a1 b1
1 a3 b3
Select those rows of df1 which index values i1 and i2 have the same values as the columns i1 and i12 in df2 resulting in:
c
i1 i2
a1 b1 1
a3 b3 3