How can I reorder multi-indexed dataframe columns at a specific level

There is a very simple way: just create a new dataframe based on the original, with the correct order of multiindex columns:

multi_tuples = [('IWWGCW',24), ('IWWGCW',48), ('IWWGDW',24), ('IWWGDW',48)
    , ('BASE',24), ('BASE',48)]

multi_cols = pd.MultiIndex.from_tuples(multi_tuples, names=['Experiment', 'Lead Time'])

df_ordered_multi_cols = pd.DataFrame(df_ori, columns=multi_cols)

This is the simplest one that worked for me:

1. for your selected level, create a list with columns in desired order;

2. reindex your columns and create a MultiIndex object from that list, keep in mind this returns a tuple;

3. use the MultiIndex object to reorder your DataFrame.

cols = ['IWWGCW', 'IWWGDW', 'BASE']
new_cols = df.columns.reindex(cols, level=0)
df.reindex(columns=new_cols[0]) #new_cols is a single item tuple

In one line:

df.reindex(columns=df.columns.reindex(['IWWGCW', 'IWWGDW', 'BASE'], level=0)[0])

voilá