id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
749924639,MDU6SXNzdWU3NDk5MjQ2Mzk=,4607,"set_index(..., append=True) act as with append=False with 'Dimensions without coordinates'",19285200,open,0,,,0,2020-11-24T17:59:49Z,2020-11-24T19:37:04Z,,NONE,,,,"**What happened**:

I get into this strange behaviour when trying to recreate a stacked (MultiIndex) coordinate using `set_index(...,append=True)`. 

Since it is not possible to save Dataset to netCDF or Zarr containing stacked / MultiIndex coordinates, before writing to disk I used `reset_index(<stacked_coordinate>)`. When reading such data, I need to use `set_index(.., append=True)` to recreate such stacked coordinate.

**What you expected to happen**:

I would expect that `set_index(..., append=True)` would recreate the MultiIndex stacked coordinate. However, this does not occur if the dimension coordinate specified within set_index() is a 'dimension without coordinate'.
In such situation, `set_index(..., append=True)` behaves as `set_index(, append=False)`.

**Minimal Complete Verifiable Example**:

```python
import xarray as xr 
import numpy as np

### Create Datasets 
arr1 = np.random.rand(4, 5).reshape(4,5)
arr2 = np.random.rand(4, 5).reshape(4,5)
da1 = xr.DataArray(arr1, 
                   dims=['nodes','time'],
                   coords={""time"": [1,2,3,4,5],
                           ""nodes"": [1,2,3,4]},
                   name='var1')
da2 = xr.DataArray(arr2, 
                   dims=['nodes','time'],
                   coords={""time"": [1,2,3,4,5],
                           ""nodes"": [1,2,3,4]},
                   name='var2')
ds_unstacked = xr.Dataset({'var1':da1,'var2':da2})
print(ds_unstacked) 

# - Stack variables across a new dimension 
da_stacked = ds_unstacked.to_stacked_array(new_dim=""variables"", variable_dim='variable', 
                                           sample_dims=['nodes','time'], name=""Stacked_Variables"") 
ds_stacked = da_stacked.to_dataset()

# - Look at the stacked MultiIndex coordinate 'variables'
print(ds_stacked) 
print(da_stacked.variables.indexes)

### Remove MultiIndex (to save Dataset to netCDF/Zarr, ...)
ds_stacked_disk = ds_stacked.reset_index('variables')
print(ds_stacked_disk)
 
### Try to recreate MultiIndex  
print(ds_stacked_disk.set_index(variables=['variable'], append=False)) # GOOD ! Replace 'variable'  coordinate with 'variables'
print(ds_stacked_disk.set_index(variables=['variable'], append=True)) # BUG ! Do not create the expected MultiIndex !  

### Current workaround to obtain a MultiIndex stacked coordinate
tmp_ds = ds_stacked_disk.assign_coords(variables=(np.arange(0,2)))
ds_stacked1 = tmp_ds.set_index(variables=['variable'], append=True)   
print(ds_stacked1)  # But with level 0 - 'variables_level_0'

### Unstack back  
# - If the BUG is solved, no need to specify the level argument  
ds_stacked1['Stacked_Variables'].to_unstacked_dataset(dim='variables', level='variable')

```

**Environment**:

<details><summary>Output of <tt>xr.show_versions()</tt></summary>

INSTALLED VERSIONS
------------------
commit: None
python: 3.8.5 | packaged by conda-forge | (default, Sep 24 2020, 16:55:52) 
[GCC 7.5.0]
python-bits: 64
OS: Linux
OS-release: 5.4.0-48-generic
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: en_US.UTF-8
libhdf5: 1.10.6
libnetcdf: 4.7.4

xarray: 0.16.1
pandas: 1.1.2
numpy: 1.19.1
scipy: 1.5.2
netCDF4: 1.5.4
pydap: None
h5netcdf: None
h5py: 2.10.0
Nio: None
zarr: 2.5.0
cftime: 1.2.1
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: 0.9.8.4
iris: None
bottleneck: 1.3.2
dask: 2.27.0
distributed: 2.27.0
matplotlib: 3.3.2
cartopy: 0.18.0
seaborn: None
numbagg: None
pint: None
setuptools: 49.6.0.post20200917
pip: 20.2.3
conda: None
pytest: None
IPython: 7.18.1
sphinx: 3.2.1


</details>
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