I found it really hard to predict the results produced by pandas.tseries.offsets, especially when n==0. Below is an example with MonthEnd and MonthBegin.

import pandas as pd
from pandas.tseries.offsets import MonthEnd, MonthBegin

date_ = pd.to_datetime('20240601')
print(date_ + MonthBegin(0))  # 2024-06-01 00:00:00
print(date_ - MonthBegin(0))  # 2024-06-01 00:00:00
print(date_ + MonthBegin(1))  # 2024-07-01 00:00:00
print(date_ - MonthBegin(1))  # 2024-05-01 00:00:00
print(date_ + MonthEnd(0))  # 2024-06-30 00:00:00
print(date_ - MonthEnd(0))  # 2024-06-30 00:00:00
print(date_ + MonthEnd(1))  # 2024-06-30 00:00:00
print(date_ - MonthEnd(1))  # 2024-05-31 00:00:00
print('n')

date_ = pd.to_datetime('20240615')
print(date_ + MonthBegin(0))  # 2024-07-01 00:00:00
print(date_ - MonthBegin(0))  # 2024-07-01 00:00:00
print(date_ + MonthBegin(1))  # 2024-07-01 00:00:00
print(date_ - MonthBegin(1))  # 2024-06-01 00:00:00
print(date_ + MonthEnd(0))  # 2024-06-30 00:00:00
print(date_ - MonthEnd(0))  # 2024-06-30 00:00:00
print(date_ + MonthEnd(1))  # 2024-06-30 00:00:00
print(date_ - MonthEnd(1))  # 2024-05-31 00:00:00
print('n')

date_ = pd.to_datetime('20240630')
print(date_ + MonthBegin(0))  # 2024-07-01 00:00:00
print(date_ - MonthBegin(0))  # 2024-07-01 00:00:00
print(date_ + MonthBegin(1))  # 2024-07-01 00:00:00
print(date_ - MonthBegin(1))  # 2024-06-01 00:00:00
print(date_ + MonthEnd(0))  # 2024-06-30 00:00:00
print(date_ - MonthEnd(0))  # 2024-06-30 00:00:00
print(date_ + MonthEnd(1))  # 2024-07-31 00:00:00
print(date_ - MonthEnd(1))  # 2024-05-31 00:00:00

If I have to add an if MonthBegin().is_month_end(date_) else ... before? If there is a way can simplify the logic and make the results predictable? e.g.

for date_ in ['20240601','20240615','20240630']:
    # In a word, `n==0` indicates this month, `n==-1` means the previous month and `n==1` means the next month.
    date_= pd.to_datetime(date_)
    print(date_ + MonthBegin(0))  # == 2024-06-01 00:00:00
    print(date_ - MonthBegin(0))  # == 2024-06-01 00:00:00
    print(date_ + MonthBegin(1))  # == 2024-07-01 00:00:00
    print(date_ - MonthBegin(1))  # == 2024-05-01 00:00:00
    print(date_ + MonthEnd(0))  # == 2024-06-30 00:00:00
    print(date_ - MonthEnd(0))  # == 2024-06-30 00:00:00
    print(date_ + MonthEnd(1))  # == 2024-07-31 00:00:00
    print(date_ - MonthEnd(1))  # == 2024-05-31 00:00:00