My question is an expansion of the one answered here:

Adding two pandas dataframes

Assuming the same dataframes but with a new column containing strings.

import pandas as pd

df1 = pd.DataFrame([('Dog',1,2),('Cat',3,4),('Rabbit',5,6)], columns=['Animal','a','b'])

df2 = pd.DataFrame([('Dog',100,200),('Cat',300,400),('Rabbit',500,600)], columns=['Animal','a','b']

Using the solution would create this:

df_add = df1.add(df2, fill_value=0)

Out: 

       Animal        a    b
    0  DogDog       101  202
    1  CatCat       303  404
    2  RabbitRabbit 505  606

A potential solution could be just to index the Animal column and then run the .add function and then unindex the animal column again. But is there a more simple way that just adjusts this formula df_add = df1.add(df2, fill_value=0)so that the following solution is given:

Out: 

       Animal     a    b
    0  Dog       101  202
    1  Cat       303  404
    2  Rabbit    505  606

I tried df_add.iloc[:,1:] = df1.iloc[:,1:].add(df2.iloc[:,1:], fill_value=0) and it did not work.