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When converting a DataFrame between JSON and CSV formats, the multi-index can be maintained by setting the appropriate parameters:

• To export a multi-index DataFrame to JSON format, use the .to_json() method with the orient='records' parameter. This will export the DataFrame as a list of dictionaries, where each dictionary represents a row and its keys correspond to the column names and the index levels with a hierarchical key name.
• To import a multi-index DataFrame from JSON format into a DataFrame, use the pandas.json_normalize() function with the appropriate record_path, meta, and record_prefix parameters to flatten the hierarchical JSON structure into a DataFrame with a multi-index.
• To export a multi-index DataFrame to CSV format, use the .to_csv() method with the header=True and index=True parameters. The index levels will be separated by a comma in the header row and in the corresponding rows of the DataFrame.
• To import a multi-index DataFrame from CSV format into a DataFrame, use the index_col parameter with a list of integers or strings that correspond to the index levels. For example, index_col=[0,1] will create a multi-index with the first and second columns as the index levels.