Sum all combinations of 2 columns from 2 dataframes
Solution 1:
Use MultiIndex.from_product for all combinations and sum DataFrames with repeated values by DataFrame.reindex:
mux = pd.MultiIndex.from_product([df1.columns, df2.columns])
df = df1.reindex(mux, level=0, axis=1) + df2.reindex(mux, level=1, axis=1)
df.columns = range(len(df.columns))
Solution 2:
IIUC you can do this with numpy.
>>> import numpy as np
>>> n = df1.shape[1]
>>> pd.DataFrame(df1.values.repeat(n) + np.tile(df2.values, n))
0 1 2 3
0 11 12 21 22