How to plot a pie plot inside a donut plot

You could adapt the example code of matplotlib's pie chart example. For the values in the donut, you can concatenate all column values (reversed to have 'A' at the left) and use three times the dataframe's index (also reversed).

import matplotlib.pyplot as plt
import pandas as pd
from io import StringIO

data_str = ''',H,E,C
A,8393.0,2872.0,5649.0
R,4360.0,2188.0,3892.0
N,2029.0,1137.0,4714.0
D,3234.0,1436.0,6761.0
C,754.0,743.0,1185.0
Q,3529.0,1278.0,2844.0
E,6649.0,2053.0,5248.0
G,2338.0,2200.0,10054.0
H,1389.0,1006.0,2112.0
I,4348.0,4210.0,2734.0
L,8642.0,4386.0,5590.0
K,4805.0,2194.0,4895.0
M,1884.0,913.0,1459.0
F,2767.0,2377.0,2601.0
P,1397.0,987.0,6678.0
S,3136.0,2226.0,6094.0
T,2986.0,2884.0,4950.0
W,987.0,787.0,930.0
Y,2218.0,2145.0,2205.0
V,4689.0,5950.0,3699.0'''
ss_dist_df = pd.read_csv(StringIO(data_str), index_col=0)
plt.figure(figsize=(10, 10))
plt.pie(ss_dist_df.sum(), labels=ss_dist_df.columns, labeldistance=0.5, textprops={'size': 16},
        radius=0.7, startangle=0, colors=['skyblue', 'salmon', 'lightgreen'])
plt.pie(list(ss_dist_df['H'][::-1]) + list(ss_dist_df['E'][::-1]) + list(ss_dist_df['C'][::-1]),
        labels=3 * list(ss_dist_df.index[::-1]),
        colors=plt.cm.tab20.colors,
        labeldistance=0.9, textprops={'size': 8},
        wedgeprops=dict(width=0.28), startangle=0)
plt.show()