diff --git a/babel/messages/extract.py b/babel/messages/extract.py
index b6dce6f..4fc3da7 100644
--- a/babel/messages/extract.py
+++ b/babel/messages/extract.py
@@ -55,7 +55,8 @@ if TYPE_CHECKING:
         def seek(self, __offset: int, __whence: int = ...) -> int: ...
         def tell(self) -> int: ...
 
-    _Keyword: TypeAlias = tuple[int | tuple[int, int] | tuple[int, str], ...] | None
+    _SimpleKeyword: TypeAlias = tuple[int | tuple[int, int] | tuple[int, str], ...] | None
+    _Keyword: TypeAlias = dict[int | None, _SimpleKeyword] | _SimpleKeyword
 
     # 5-tuple of (filename, lineno, messages, comments, context)
     _FileExtractionResult: TypeAlias = tuple[str, int, str | tuple[str, ...], list[str], str | None]
@@ -315,6 +316,47 @@ def extract_from_file(
                             options, strip_comment_tags))
 
 
+def _match_messages_against_spec(lineno: int, messages: list[str|None], comments: list[str],
+                                 fileobj: _FileObj, spec: tuple[int|tuple[int, str], ...]):
+    translatable = []
+    context = None
+
+    # last_index is 1 based like the keyword spec
+    last_index = len(messages)
+    for index in spec:
+        if isinstance(index, tuple): # (n, 'c')
+            context = messages[index[0] - 1]
+            continue
+        if last_index < index:
+            # Not enough arguments
+            return
+        message = messages[index - 1]
+        if message is None:
+            return
+        translatable.append(message)
+
+    # keyword spec indexes are 1 based, therefore '-1'
+    if isinstance(spec[0], tuple):
+        # context-aware *gettext method
+        first_msg_index = spec[1] - 1
+    else:
+        first_msg_index = spec[0] - 1
+    # An empty string msgid isn't valid, emit a warning
+    if not messages[first_msg_index]:
+        filename = (getattr(fileobj, "name", None) or "(unknown)")
+        sys.stderr.write(
+            f"{filename}:{lineno}: warning: Empty msgid.  It is reserved by GNU gettext: gettext(\"\") "
+            f"returns the header entry with meta information, not the empty string.\n"
+        )
+        return
+
+    translatable = tuple(translatable)
+    if len(translatable) == 1:
+        translatable = translatable[0]
+
+    return lineno, translatable, comments, context
+
+
 def extract(
     method: _ExtractionMethod,
     fileobj: _FileObj,
@@ -400,56 +442,30 @@ def extract(
                    options=options or {})
 
     for lineno, funcname, messages, comments in results:
-        spec = keywords[funcname] or (1,) if funcname else (1,)
         if not isinstance(messages, (list, tuple)):
             messages = [messages]
         if not messages:
             continue
 
-        # Validate the messages against the keyword's specification
-        context = None
-        msgs = []
-        invalid = False
-        # last_index is 1 based like the keyword spec
-        last_index = len(messages)
-        for index in spec:
-            if isinstance(index, tuple):
-                context = messages[index[0] - 1]
-                continue
-            if last_index < index:
-                # Not enough arguments
-                invalid = True
-                break
-            message = messages[index - 1]
-            if message is None:
-                invalid = True
-                break
-            msgs.append(message)
-        if invalid:
-            continue
-
-        # keyword spec indexes are 1 based, therefore '-1'
-        if isinstance(spec[0], tuple):
-            # context-aware *gettext method
-            first_msg_index = spec[1] - 1
-        else:
-            first_msg_index = spec[0] - 1
-        if not messages[first_msg_index]:
-            # An empty string msgid isn't valid, emit a warning
-            filename = (getattr(fileobj, "name", None) or "(unknown)")
-            sys.stderr.write(
-                f"{filename}:{lineno}: warning: Empty msgid.  It is reserved by GNU gettext: gettext(\"\") "
-                f"returns the header entry with meta information, not the empty string.\n"
-            )
-            continue
-
-        messages = tuple(msgs)
-        if len(messages) == 1:
-            messages = messages[0]
+        specs = keywords[funcname] or None if funcname else None
+        # {None: x} may be collapsed into x for backwards compatibility.
+        if not isinstance(specs, dict):
+            specs = {None: specs}
 
         if strip_comment_tags:
             _strip_comment_tags(comments, comment_tags)
-        yield lineno, messages, comments, context
+
+        # None matches all arities.
+        for arity in (None, len(messages)):
+            try:
+                spec = specs[arity]
+            except KeyError:
+                continue
+            if spec is None:
+                spec = (1,)
+            result = _match_messages_against_spec(lineno, messages, comments, fileobj, spec)
+            if result is not None:
+                yield result
 
 
 def extract_nothing(
diff --git a/babel/messages/frontend.py b/babel/messages/frontend.py
index 6ed1fe5..0008a9b 100644
--- a/babel/messages/frontend.py
+++ b/babel/messages/frontend.py
@@ -8,6 +8,8 @@
     :license: BSD, see LICENSE for more details.
 """
 
+from __future__ import annotations
+
 import datetime
 import fnmatch
 import logging
@@ -1111,34 +1113,63 @@ def parse_mapping(fileobj, filename=None):
 
     return method_map, options_map
 
+def _parse_spec(s: str) -> tuple[int | None, tuple[int|tuple[int, str], ...]]:
+    inds = []
+    number = None
+    for x in s.split(','):
+        if x[-1] == 't':
+            number = int(x[:-1])
+        elif x[-1] == 'c':
+            inds.append((int(x[:-1]), 'c'))
+        else:
+            inds.append(int(x))
+    return number, tuple(inds)
 
 def parse_keywords(strings: Iterable[str] = ()):
     """Parse keywords specifications from the given list of strings.
 
-    >>> kw = sorted(parse_keywords(['_', 'dgettext:2', 'dngettext:2,3', 'pgettext:1c,2']).items())
-    >>> for keyword, indices in kw:
-    ...     print((keyword, indices))
-    ('_', None)
-    ('dgettext', (2,))
-    ('dngettext', (2, 3))
-    ('pgettext', ((1, 'c'), 2))
+    >>> import pprint
+    >>> keywords = ['_', 'dgettext:2', 'dngettext:2,3', 'pgettext:1c,2',
+    ...             'polymorphic:1', 'polymorphic:2,2t', 'polymorphic:3c,3t']
+    >>> pprint.pprint(parse_keywords(keywords))
+    {'_': None,
+     'dgettext': (2,),
+     'dngettext': (2, 3),
+     'pgettext': ((1, 'c'), 2),
+     'polymorphic': {None: (1,), 2: (2,), 3: ((3, 'c'),)}}
+
+    The input keywords are in GNU Gettext style; see :doc:`cmdline` for details.
+
+    The output is a dictionary mapping keyword names to a dictionary of specifications.
+    Keys in this dictionary are numbers of arguments, where ``None`` means that all numbers
+    of arguments are matched, and a number means only calls with that number of arguments
+    are matched (which happens when using the "t" specifier). However, as a special
+    case for backwards compatibility, if the dictionary of specifications would
+    be ``{None: x}``, i.e., there is only one specification and it matches all argument
+    counts, then it is collapsed into just ``x``.
+
+    A specification is either a tuple or None. If a tuple, each element can be either a number
+    ``n``, meaning that the nth argument should be extracted as a message, or the tuple
+    ``(n, 'c')``, meaning that the nth argument should be extracted as context for the
+    messages. A ``None`` specification is equivalent to ``(1,)``, extracting the first
+    argument.
     """
     keywords = {}
     for string in strings:
         if ':' in string:
-            funcname, indices = string.split(':')
+            funcname, spec_str = string.split(':')
+            number, spec = _parse_spec(spec_str)
         else:
-            funcname, indices = string, None
-        if funcname not in keywords:
-            if indices:
-                inds = []
-                for x in indices.split(','):
-                    if x[-1] == 'c':
-                        inds.append((int(x[:-1]), 'c'))
-                    else:
-                        inds.append(int(x))
-                indices = tuple(inds)
-            keywords[funcname] = indices
+            funcname = string
+            number = None
+            spec = None
+        keywords.setdefault(funcname, {})[number] = spec
+
+    # For best backwards compatibility, collapse {None: x} into x.
+    for k, v in keywords.items():
+        if set(v) == {None}:
+            keywords[k] = v[None]
+
     return keywords
 
 
diff --git a/docs/cmdline.rst b/docs/cmdline.rst
index 8d9742f..e1328fe 100644
--- a/docs/cmdline.rst
+++ b/docs/cmdline.rst
@@ -133,6 +133,45 @@ a collection of source files::
                             header comment for the catalog
 
 
+The meaning of ``--keyword`` values is as follows:
+
+- Pass a simple identifier like ``_`` to extract the first (and only the first)
+  argument of all function calls to ``_``,
+
+- To extract other arguments than the first, add a colon and the argument
+  indices separated by commas. For example, the ``dngettext`` function
+  typically expects translatable strings as second and third arguments,
+  so you could pass ``dngettext:2,3``.
+
+- Some arguments should not be interpreted as translatable strings, but
+  context strings. For that, append "c" to the argument index. For example:
+  ``pgettext:1c,2``.
+
+- In C++ and Python, you may have functions that behave differently
+  depending on how many arguments they take. For this use case, you can
+  add an integer followed by "t" after the colon. In this case, the
+  keyword will only match a function invocation if it has the specified
+  total number of arguments.  For example, if you have a function
+  ``foo`` that behaves as ``gettext`` (argument is a message) or
+  ``pgettext`` (arguments are a context and a message) depending on
+  whether it takes one or two arguments, you can pass
+  ``--keyword=foo:1,1t --keyword=foo:1c,2,2t``.
+
+The default keywords are equivalent to passing ::
+
+  --keyword=_
+  --keyword=gettext
+  --keyword=ngettext:1,2
+  --keyword=ugettext
+  --keyword=ungettext:1,2
+  --keyword=dgettext:2
+  --keyword=dngettext:2,3
+  --keyword=N_
+  --keyword=pgettext:1c,2
+  --keyword=npgettext:1c,2,3
+
+
+
 init
 ====
 

diff --git a/tests/messages/test_frontend.py b/tests/messages/test_frontend.py
index 821738d..b28cb0d 100644
--- a/tests/messages/test_frontend.py
+++ b/tests/messages/test_frontend.py
@@ -17,7 +17,7 @@ import sys
 import time
 import unittest
 from datetime import datetime, timedelta
-from io import StringIO
+from io import BytesIO, StringIO
 
 import pytest
 from freezegun import freeze_time
@@ -25,7 +25,7 @@ from setuptools import Distribution
 
 from babel import __version__ as VERSION
 from babel.dates import format_datetime
-from babel.messages import Catalog, frontend
+from babel.messages import Catalog, extract, frontend
 from babel.messages.frontend import (
     BaseError,
     CommandLineInterface,
@@ -1422,6 +1422,35 @@ def test_parse_keywords():
     }
 
 
+def test_parse_keywords_with_t():
+    kw = frontend.parse_keywords(['_:1', '_:2,2t', '_:2c,3,3t'])
+
+    assert kw == {
+        '_': {
+            None: (1,),
+            2: (2,),
+            3: ((2, 'c'), 3),
+        }
+    }
+
+def test_extract_messages_with_t():
+    content = rb"""
+_("1 arg, arg 1")
+_("2 args, arg 1", "2 args, arg 2")
+_("3 args, arg 1", "3 args, arg 2", "3 args, arg 3")
+_("4 args, arg 1", "4 args, arg 2", "4 args, arg 3", "4 args, arg 4")
+"""
+    kw = frontend.parse_keywords(['_:1', '_:2,2t', '_:2c,3,3t'])
+    result = list(extract.extract("python", BytesIO(content), kw))
+    expected = [(2, '1 arg, arg 1', [], None),
+                (3, '2 args, arg 1', [], None),
+                (3, '2 args, arg 2', [], None),
+                (4, '3 args, arg 1', [], None),
+                (4, '3 args, arg 3', [], '3 args, arg 2'),
+                (5, '4 args, arg 1', [], None)]
+    assert result == expected
+
+
 def configure_cli_command(cmdline):
     """
     Helper to configure a command class, but not run it just yet.

Feature request: Support gettext-like "t" specifier in keywords
The full description of xgettext's `--keyword` option is [here](https://www.gnu.org/software/gettext/manual/html_node/xgettext-Invocation.html#Language-specific-options).

`pybabel extract` supports a similar syntax, but it does not support the trailing "*n*t" to indicate that this keyword only applies when there are *n* arguments. This can be useful in some Python projects ([example](https://github.com/frescobaldi/frescobaldi)) where the `_` function is variadic for convenience. (In this particular project, it behaves like `gettext` with 1 arg, `pgettext` with 2 args, `ngettext` with 3 args and `npgettext` with 4 args, i.e., `_(message)`, `_(context, message)`, `_(singular, plural, number)` or `_(context, singular, plural, number)`.)
tests/messages/test_frontend.py::test_parse_keywords_with_t tests/messages/test_frontend.py::test_extract_messages_with_t
tests/messages/test_frontend.py::CompileCatalogTestCase::test_no_directory_or_input_file_specified tests/messages/test_frontend.py::CompileCatalogTestCase::test_no_directory_or_output_file_specified tests/messages/test_frontend.py::ExtractMessagesTestCase::test_both_sort_output_and_sort_by_file tests/messages/test_frontend.py::ExtractMessagesTestCase::test_input_dirs_is_alias_for_input_paths tests/messages/test_frontend.py::ExtractMessagesTestCase::test_input_dirs_is_mutually_exclusive_with_input_paths tests/messages/test_frontend.py::ExtractMessagesTestCase::test_input_paths_handle_spaces_after_comma tests/messages/test_frontend.py::ExtractMessagesTestCase::test_invalid_file_or_dir_input_path tests/messages/test_frontend.py::ExtractMessagesTestCase::test_neither_default_nor_custom_keywords tests/messages/test_frontend.py::ExtractMessagesTestCase::test_no_output_file_specified tests/messages/test_frontend.py::InitCatalogTestCase::test_no_input_file tests/messages/test_frontend.py::InitCatalogTestCase::test_no_locale tests/messages/test_frontend.py::CommandLineInterfaceTestCase::test_help tests/messages/test_frontend.py::CommandLineInterfaceTestCase::test_usage tests/messages/test_frontend.py::test_parse_mapping tests/messages/test_frontend.py::test_parse_keywords tests/messages/test_frontend.py::test_extract_keyword_args_384[-k-False] tests/messages/test_frontend.py::test_extract_keyword_args_384[-k-True] tests/messages/test_frontend.py::test_extract_keyword_args_384[--keyword-False] tests/messages/test_frontend.py::test_extract_keyword_args_384[--keyword-True] tests/messages/test_frontend.py::test_extract_keyword_args_384[--keywords-False] tests/messages/test_frontend.py::test_extract_keyword_args_384[--keywords-True] tests/messages/test_frontend.py::test_extract_distutils_keyword_arg_388[LW_-expected0] tests/messages/test_frontend.py::test_extract_distutils_keyword_arg_388[LW_ tests/messages/test_frontend.py::test_extract_distutils_keyword_arg_388[yiy tests/messages/test_frontend.py::test_extract_cli_knows_dash_s tests/messages/test_frontend.py::test_extract_add_location