Of course, we can come up with a solution where we will use 'c4', but I see the solution this way.

We can bring to the form you need with the help of an auxiliary column 'group'. It will help us to index the values for future transformation.

Now we will write a function that will create a pd.Series. We take the values and place them into one array using flatten().

def grouping(g):
    return pd.Series(g[['c1', 'c2', 'c3']].values.flatten(), 
                     index=[f'c{i+1}' for i in range(9)])

We apply the function to the grouped DataFrame by the auxiliary column 'group'.

Full code:

import pandas as pd

data = {
    'c1': [1, 10, 100, 1, 10, 100],
    'c2': [2, 20, 200, 2, 20, 200],
    'c3': [3, 30, 300, 3, 30, 300],
    'c4': [0, 1, 2, 0, 1, 2]
}

df = pd.DataFrame(data)

df['group'] = df.index // 3

def grouping(g):
    return pd.Series(g[['c1', 'c2', 'c3']].values.flatten(), 
                     index=[f'c{i+1}' for i in range(9)])

transformed_df = df.groupby('group').apply(grouping).reset_index(drop=True)