I believe this does what you are after:
df.groupby(lambda x:x, axis=1).sum()
Alternatively, between 3% and 15% faster depending on the length of the df:
df.groupby(df.columns, axis=1).sum()
EDIT: To extend this beyond sums, use .agg() (short for .aggregate()):
df.groupby(df.columns, axis=1).agg(numpy.max)