On 1.5.x:

df = pd.DataFrame({'a': [1, 1, 2], 'b': [3, 4, 5]}).set_index(['a', 'b'])

print(df.index.isin([]))
# [False False False]

On 2.0.x:

TypeError: Cannot infer number of levels from empty list

Seems like an Index consisting of False is the right answer here.

Comment From: rhshadrach

commit 02d988ca8f5be9ffe8435b7f37c4dd8d43ccd108
Author: Patrick Hoefler
Date:   Tue Sep 20 00:58:34 2022 +0200

    PERF: Improve performance for MultiIndex.isin (#48622)

    * PERF: Improve performance for MultiIndex.isin

    * PERF: Improve performance for MultiIndex.isin

    * Fix gh ref

 asv_bench/benchmarks/multiindex_object.py | 32 +++++++++++++++++++++++++++++++
 doc/source/whatsnew/v1.6.0.rst            |  1 +
 pandas/core/indexes/multi.py              |  3 +--
 3 files changed, 34 insertions(+), 2 deletions(-)

cc @phofl