diff --git a/Doc/library/email.policy.rst b/Doc/library/email.policy.rst
--- a/Doc/library/email.policy.rst
+++ b/Doc/library/email.policy.rst
@@ -196,6 +196,25 @@
       custom ``Message`` objects) should also provide such an attribute,
       otherwise defects in parsed messages will raise unexpected errors.
 
+   .. method:: header_max_count(name)
+
+      Return the maximum allowed number of headers named *name*.
+
+      Called when a header is added to a :class:`~email.message.Message`
+      object.  If the returned value is not ``0`` or ``None``, and there are
+      already a number of headers with the name *name* equal to the value
+      returned, a :exc:`ValueError` is raised.
+
+      Because the default behavior of ``Message.__setitem__`` is to append the
+      value to the list of headers, it is easy to create duplicate headers
+      without realizing it.  This method allows certain headers to be limited
+      in the number of instances of that header that may be added to a
+      ``Message`` programmatically.  (The limit is not observed by the parser,
+      which will faithfully produce as many headers as exist in the message
+      being parsed.)
+
+      The default implementation returns ``None`` for all header names.
+
    .. method:: header_source_parse(sourcelines)
 
       The email package calls this method with a list of strings, each string
@@ -366,6 +385,12 @@
    The class provides the following concrete implementations of the abstract
    methods of :class:`Policy`:
 
+   .. method:: header_max_count(name)
+
+      Returns the value of the
+      :attr:`~email.headerregistry.BaseHeader.max_count` attribute of the
+      specialized class used to represent the header with the given name.
+
    .. method:: header_source_parse(sourcelines)
 
       The implementation of this method is the same as that for the
diff --git a/Lib/email/_policybase.py b/Lib/email/_policybase.py
--- a/Lib/email/_policybase.py
+++ b/Lib/email/_policybase.py
@@ -194,6 +194,25 @@
         """
         obj.defects.append(defect)
 
+    def header_max_count(self, name):
+        """Return the maximum allowed number of headers named 'name'.
+
+        Called when a header is added to a Message object.  If the returned
+        value is not 0 or None, and there are already a number of headers with
+        the name 'name' equal to the value returned, a ValueError is raised.
+
+        Because the default behavior of Message's __setitem__ is to append the
+        value to the list of headers, it is easy to create duplicate headers
+        without realizing it.  This method allows certain headers to be limited
+        in the number of instances of that header that may be added to a
+        Message programmatically.  (The limit is not observed by the parser,
+        which will faithfully produce as many headers as exist in the message
+        being parsed.)
+
+        The default implementation returns None for all header names.
+        """
+        return None
+
     @abc.abstractmethod
     def header_source_parse(self, sourcelines):
         """Given a list of linesep terminated strings constituting the lines of
diff --git a/Lib/email/message.py b/Lib/email/message.py
--- a/Lib/email/message.py
+++ b/Lib/email/message.py
@@ -346,6 +346,16 @@
         Note: this does not overwrite an existing header with the same field
         name.  Use __delitem__() first to delete any existing headers.
         """
+        max_count = self.policy.header_max_count(name)
+        if max_count:
+            lname = name.lower()
+            found = 0
+            for k, v in self._headers:
+              if k.lower() == lname:
+                found += 1
+                if found >= max_count:
+                    raise ValueError("There may be at most {} {} headers "
+                                     "in a message".format(max_count, name))
         self._headers.append(self.policy.header_store_parse(name, val))
 
     def __delitem__(self, name):
diff --git a/Lib/email/policy.py b/Lib/email/policy.py
--- a/Lib/email/policy.py
+++ b/Lib/email/policy.py
@@ -109,6 +109,13 @@
                              "or carriage return characters")
         return (name, self.header_factory(name, value))
 
+    def header_max_count(self, name):
+        """+
+        Returns the max_count attribute from the specialized header class
+        that would be used to construct a header of type 'name'.
+        """
+        return self.header_factory[name].max_count
+
     def header_fetch_parse(self, name, value):
         """+
         If the value has a 'name' attribute, it is returned to unmodified.
diff --git a/Lib/test/test_email/test_message.py b/Lib/test/test_email/test_message.py
new file mode 100644
--- /dev/null
+++ b/Lib/test/test_email/test_message.py
@@ -0,0 +1,18 @@
+import unittest
+from email import policy
+from test.test_email import TestEmailBase
+
+
+class Test(TestEmailBase):
+
+    policy = policy.default
+
+    def test_error_on_setitem_if_max_count_exceeded(self):
+        m = self._str_msg("")
+        m['To'] = 'abc@xyz'
+        with self.assertRaises(ValueError):
+            m['To'] = 'xyz@abc'
+
+
+if __name__ == '__main__':
+    unittest.main()