creating a conditional column in a multi-level dataframe

import pandas as pd
import numpy as np

level_2 = ['X', 'Y', 'X', 'Y', 'X', 'Y']
level_1 = ['A', 'A', 'B', 'B', 'C', 'C']

data = [['a1', 2, 'b1', 4, 'c1', 3], ['a2', 16, 'b2', 48, 'c2', 78], ['a3', 10, 'b3', 12, 'c3', 34], ['a4', 114, 'b4', 6, 'c4', 1]]

columns = pd.MultiIndex.from_tuples(list(zip(level_1, level_2)))

df = pd.DataFrame(data, columns=columns)

I'm very new to python, so apologies for the basic nature of the question. I have the above dataframe. I would like to create another 2 columns based on the 2 greatest numbers in column [A][Y] or [B][Y] or [C][Y] and then select the corresponding column [A][X] or [B][X] or [C][X]. Any help would be greatly appreciated.

I've tried argsort but haven't been able to figure out how to reference the correct corresponding column.

Maybe not the prettiest solution but it gets job done (the main function is Series.nlargest):

def fn(x):
    x = x.nlargest(2)

    a, b = x
    ia, ib = x.index

    return {
        ("Greatest1", "X"): f"{df_x.loc[x.name, ia]}",
        ("Greatest1", "Y"): a,
        ("Greatest2", "X"): f"{df_x.loc[x.name, ib]}",
        ("Greatest2", "Y"): b,
    }

df_x = df.xs("X", axis=1, level=1)
x = df.xs("Y", axis=1, level=1).apply(fn, axis=1, result_type="expand")
df = pd.concat([df, x], axis=1)
print(df)

Prints:

    A        B       C     Greatest1      Greatest2    
    X    Y   X   Y   X   Y         X    Y         X   Y
0  a1    2  b1   4  c1   3        b1    4        c1   3
1  a2   16  b2  48  c2  78        c2   78        b2  48
2  a3   10  b3  12  c3  34        c3   34        b3  12
3  a4  114  b4   6  c4   1        a4  114        b4   6

Another possible option :

NBOG = 2
lvl1 = df.columns.levels[1]
lst2 = [[f"Greatest{i+1}" for i in range(NBOG)], lvl1]

arrg = (
    df.stack(0).set_index(lvl1[0], append=True)
        .groupby(level=0, group_keys=False)[lvl1[1]]
        .nlargest(NBOG).droplevel(0).reset_index(level=1)
        .to_numpy().reshape(-1, len(lvl1)*NBOG)
)

out = df.join(pd.DataFrame(arrg, columns=pd.MultiIndex.from_product(lst2)))

Ouptut :

print(out)

    A        B       C     Greatest1      Greatest2    
    X    Y   X   Y   X   Y         X    Y         X   Y
0  a1    2  b1   4  c1   3        b1    4        c1   3
1  a2   16  b2  48  c2  78        c2   78        b2  48
2  a3   10  b3  12  c3  34        c3   34        b3  12
3  a4  114  b4   6  c4   1        a4  114        b4   6