diff --git a/README.md b/README.md
index 0db924a..cc3d988 100644
--- a/README.md
+++ b/README.md
@@ -19,6 +19,7 @@ this issue: [#83](https://github.com/Lucas-C/pre-commit-hooks/issues/83)
     - [Handling years flexibly](#handling-years-flexibly)
     - [No extra EOL](#no-extra-eol)
     - [Fuzzy license matching](#fuzzy-license-matching)
+    - [Multiple license files](#multiple-license-files)
 - [Handy shell functions](#handy-shell-functions)
 - [Useful local hooks](#useful-local-hooks)
   - [Forbid / remove some unicode characters](#forbid--remove-some-unicode-characters)
@@ -168,6 +169,23 @@ License insertion can be skipped altogether if the file contains the
 `SKIP LICENSE INSERTION` in the first X top lines. This can also be
 overridden by `--skip-license-insertion-comment=<COMMENT>` flag.
 
+#### Multiple license files
+
+If more than one `--license-filepath` argument is specified, the checks are
+performed as follows:
+
+1. First, an exact match is pursued, checking the 1st license file, then
+   the 2nd, and so on. If a match is found, the normal behavior is
+   followed, as if the matched license file was the only license file
+   specified.
+
+2. If no exact match is found, then the software resorts to fuzzy matching.
+   Again, as soon as a match is found, the normal behavior is followed, as
+   if the fuzzy-matched license file was the only license file specified.
+
+3. Finally, if neither exact nor fuzzy matches are found, the content of
+   the first license file is inserted.
+
 ## Handy shell functions
 
 ```shell
diff --git a/pre_commit_hooks/insert_license.py b/pre_commit_hooks/insert_license.py
index f265962..f9acc84 100644
--- a/pre_commit_hooks/insert_license.py
+++ b/pre_commit_hooks/insert_license.py
@@ -194,7 +194,7 @@ def get_license_info_list(args) -> list[LicenseInfo]:
     return license_info_list
 
 
-def process_files(
+def process_files(  # pylint: disable=too-many-branches
     args,
     changed_files: list[str],
     todo_files: list[str],