Given the following three Pandas data frames, I need to merge them similar to an SQL full outer join. Note that the key is multi-index type_N and id_N with N = 1,2,3:

import pandas as pdraw_data = {'type_1': [0, 1, 1,1],'id_1': ['3', '4', '5','5'],'name_1': ['Alex', 'Amy', 'Allen', 'Jane']}
df_a = pd.DataFrame(raw_data, columns = ['type_1', 'id_1', 'name_1' ])raw_datab = {'type_2': [1, 1, 1, 0],'id_2': ['4', '5', '5', '7'],'name_2': ['Bill', 'Brian', 'Joe', 'Bryce']}
df_b = pd.DataFrame(raw_datab, columns = ['type_2', 'id_2', 'name_2'])raw_datac = {'type_3': [1, 0],'id_3': ['4', '7'],'name_3': ['School', 'White']}
df_c = pd.DataFrame(raw_datac, columns = ['type_3', 'id_3', 'name_3'])

The expected result should be:

type_1   id_1   name_1   type_2   id_2   name_2   type_3   id_3   name_3
0        3      Alex     NaN      NaN    NaN      NaN      NaN    NaN
1        4      Amy      1        4      Bill     1        4      School
1        5      Allen    1        5      Brian    NaN      NaN    NaN
1        5      Allen    1        5      Joe      NaN      NaN    NaN
1        5      Jane     1        5      Brian    NaN      NaN    NaN
1        5      Jane     1        5      Joe      NaN      NaN    NaN
NaN      NaN    NaN      0        7      Bryce    0        7      White

How can this be achieved in Pandas?

I'll propose that you make life less complicated and not have different names for the things you want to merge on.

da = df_a.set_index(['type_1', 'id_1']).rename_axis(['type', 'id'])
db = df_b.set_index(['type_2', 'id_2']).rename_axis(['type', 'id'])
dc = df_c.set_index(['type_3', 'id_3']).rename_axis(['type', 'id'])da.join(db, how='outer').join(dc, how='outer')name_1 name_2  name_3
type id                      
0    3    Alex    NaN     NaN7     NaN  Bryce   White
1    4     Amy   Bill  School5   Allen  Brian     NaN5   Allen    Joe     NaN5    Jane  Brian     NaN5    Jane    Joe     NaN

Here's an obnoxious way to get those other columns

from cytoolz.dicttoolz import mergei = pd.DataFrame(d.index.values.tolist(), d.index, d.index.names)
d = d.assign(**merge(i.mask(d[f'name_{j}'].isna()).add_suffix(f'_{j}').to_dict('l')for j in [1, 2, 3]
))d[sorted(d.columns, key=lambda x: x.split('_')[::-1])]id_1 name_1  type_1 id_2 name_2  type_2 id_3  name_3  type_3
type id                                                             
0    3     3   Alex     0.0  NaN    NaN     NaN  NaN     NaN     NaN7   NaN    NaN     NaN    7  Bryce     0.0    7   White     0.0
1    4     4    Amy     1.0    4   Bill     1.0    4  School     1.05     5  Allen     1.0    5  Brian     1.0  NaN     NaN     NaN5     5  Allen     1.0    5    Joe     1.0  NaN     NaN     NaN5     5   Jane     1.0    5  Brian     1.0  NaN     NaN     NaN5     5   Jane     1.0    5    Joe     1.0  NaN     NaN     NaN