You could use pd.DateOffset
In [1756]: df.date + pd.DateOffset(months=plus_month_period)
Out[1756]:
0 2017-01-11
1 2017-02-01
Name: date, dtype: datetime64[ns]
Another way using pd.offsets.MonthOffset
In [1785]: df.date + pd.offsets.MonthOffset(plus_month_period)
Out[1785]:
0 2016-10-14
1 2016-11-04
Name: date, dtype: datetime64[ns]
Details
In [1757]: df
Out[1757]:
date
0 2016-10-11
1 2016-11-01
In [1758]: plus_month_period
Out[1758]: 3