issues: 1330149534

What happened?

After applying the concat function to a dataset with a Multiindex, a lot of functions related to indexing are broken. For example, it is not possible to apply reindex_like to itself anymore.

The error is raised in the alignment module. It seems that the function find_matching_indexes does not find indexes that belong to the same dimension.

What did you expect to happen?

I expected the alignment to be functional and that these basic functions work.

Minimal Complete Verifiable Example

```Python import xarray as xr import pandas as pd

index = pd.MultiIndex.from_product([[1,2], ['a', 'b']], names=('level1', 'level2')) index.name = 'dim'

var = xr.DataArray(1, coords=[index]) ds = xr.Dataset({"var":var})

new = xr.concat([ds], dim='newdim') xr.Dataset(new) # breaks new.reindex_like(new) # breaks ```

MVCE confirmation

• [X] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
• [X] Complete example — the example is self-contained, including all data and the text of any traceback.
• [X] Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
• [X] New issue — a search of GitHub Issues suggests this is not a duplicate.

Relevant log output

```Python Traceback (most recent call last):

File "/tmp/ipykernel_407170/4030736219.py", line 11, in <cell line: 11> xr.Dataset(new) # breaks

File "/home/fabian/.miniconda3/lib/python3.10/site-packages/xarray/core/dataset.py", line 599, in init variables, coord_names, dims, indexes, _ = merge_data_and_coords(

File "/home/fabian/.miniconda3/lib/python3.10/site-packages/xarray/core/merge.py", line 575, in merge_data_and_coords return merge_core(

File "/home/fabian/.miniconda3/lib/python3.10/site-packages/xarray/core/merge.py", line 752, in merge_core aligned = deep_align(

File "/home/fabian/.miniconda3/lib/python3.10/site-packages/xarray/core/alignment.py", line 827, in deep_align aligned = align(

File "/home/fabian/.miniconda3/lib/python3.10/site-packages/xarray/core/alignment.py", line 764, in align aligner.align()

File "/home/fabian/.miniconda3/lib/python3.10/site-packages/xarray/core/alignment.py", line 550, in align self.assert_no_index_conflict()

File "/home/fabian/.miniconda3/lib/python3.10/site-packages/xarray/core/alignment.py", line 319, in assert_no_index_conflict raise ValueError(

ValueError: cannot re-index or align objects with conflicting indexes found for the following dimensions: 'dim' (2 conflicting indexes) Conflicting indexes may occur when - they relate to different sets of coordinate and/or dimension names - they don't have the same type - they may be used to reindex data along common dimensions ```

Anything else we need to know?

No response

Environment

INSTALLED VERSIONS ------------------ commit: None python: 3.10.5 | packaged by conda-forge | (main, Jun 14 2022, 07:04:59) [GCC 10.3.0] python-bits: 64 OS: Linux OS-release: 5.15.0-41-generic machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: en_US.UTF-8 LOCALE: ('en_US', 'UTF-8') libhdf5: 1.12.1 libnetcdf: 4.8.1 xarray: 2022.6.0 pandas: 1.4.2 numpy: 1.21.6 scipy: 1.8.1 netCDF4: 1.6.0 pydap: None h5netcdf: None h5py: 3.6.0 Nio: None zarr: None cftime: 1.5.1.1 nc_time_axis: None PseudoNetCDF: None rasterio: 1.2.10 cfgrib: None iris: None bottleneck: 1.3.4 dask: 2022.6.1 distributed: 2022.6.1 matplotlib: 3.5.1 cartopy: 0.20.2 seaborn: 0.11.2 numbagg: None fsspec: 2022.3.0 cupy: None pint: None sparse: 0.13.0 flox: None numpy_groupies: None setuptools: 61.2.0 pip: 22.1.2 conda: 4.13.0 pytest: 7.1.2 IPython: 7.33.0 sphinx: 5.0.2 /home/fabian/.miniconda3/lib/python3.10/site-packages/_distutils_hack/__init__.py:30: UserWarning: Setuptools is replacing distutils. warnings.warn("Setuptools is replacing distutils.")