Pandas BUG: pd.concat() cannot concatenate more than 3 mixed-frequency dataframes with multi-index series

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Reproducible Example

n = 5
p = 2
dfA = pd.DataFrame(np.random.rand(n,p),
                   columns=['A0','B0'],
                   index=pd.period_range(start='2000-1-1',periods=n,freq='Y'))

dfQ = pd.DataFrame(np.random.rand(n,p),
                   columns=['A0','B0'],
                   index=pd.period_range(start='2000-1-1',periods=n,freq='Q'))

dfM = pd.DataFrame(np.random.rand(n,p),
                   columns=['A0','B0'],
                   index=pd.period_range(start='2000-1-1',periods=n,freq='M'))

df1 = dfA.loc[:,['A0']].T.stack()
df2 = dfA.loc[:,['B0']].T.stack()
df3 = dfQ.loc[:,['A0']].T.stack()
df4 = dfQ.loc[:,['B0']].T.stack()
df5 = dfM.loc[:,['A0']].T.stack()
df6 = dfM.loc[:,['B0']].T.stack()

# these work
pd.concat([df1,df4])
pd.concat([df1,df2])
pd.concat([df1,df3])
pd.concat([df1,df2,df3])
pd.concat([dfA['A0'],dfQ['A0'],dfM['A0']])

# error
pd.concat([df1,df3,df2])
pd.concat([df1,df2,df3,df4])
pd.concat([df1,df3,df5])

Issue Description

pd.concat() can concatenate 3 multi-index dataframes when they have 2 frequencies, but cannot concatenate 4 dataframes.

Expected Behavior

pd.concat() should be able to concatenate a list of mixed-freq multiindex dataframes no matter how many items the list has.

Installed Versions

INSTALLED VERSIONS ------------------ commit : d9cdd2ee5a58015ef6f4d15c7226110c9aab8140 python : 3.12.4.final.0 python-bits : 64 OS : Windows OS-release : 2016Server Version : 10.0.14393 machine : AMD64 processor : Intel64 Family 6 Model 85 Stepping 4, GenuineIntel byteorder : little LC_ALL : None LANG : en LOCALE : English_United States.1252 pandas : 2.2.2 numpy : 1.26.4 pytz : 2024.1 dateutil : 2.9.0.post0 setuptools : 72.1.0 pip : 24.0 Cython : 3.0.11 pytest : None hypothesis : None sphinx : 8.0.2 blosc : None feather : None xlsxwriter : None lxml.etree : None html5lib : None pymysql : None psycopg2 : None jinja2 : 3.1.4 IPython : 8.26.0 pandas_datareader : None adbc-driver-postgresql: None adbc-driver-sqlite : None bs4 : 4.12.3 bottleneck : None dataframe-api-compat : None fastparquet : None fsspec : 2024.6.1 gcsfs : None matplotlib : 3.9.1.post1 numba : None numexpr : None odfpy : None openpyxl : None pandas_gbq : None pyarrow : 17.0.0 pyreadstat : None python-calamine : None pyxlsb : None s3fs : None scipy : 1.14.0 sqlalchemy : None tables : None tabulate : 0.9.0 xarray : None xlrd : None zstandard : None tzdata : 2024.1 qtpy : 2.4.1 pyqt5 : None

Comment From: rhshadrach

Thanks for the report, agreed this looks inconsistent. I'm guessing we should raise rather than converting to object dtype. @jbrockmendel - any thoughts?