Python dict like surjective multiple key → value container

I'm currently in the need for a Python container class with similar functionality like the builtin dict type. Basically what I need is a dictionary, where an arbitrary number of keys beside a primary key, which map to the very same value. However when iterating over it, it should iterate only over the (primary_key, value) pairs and only the primary key if the list of keys is requested.

If this has already been implemented I'd rather not reinvent the wheel. So is there already a module providing such a container? If not, I'm going to implement it myself.

Here is a quick implementation:

class MultipleKeyDict(dict):
    __slots__ = ["_primary_keys"]
    def __init__(self, arg=None, **kwargs):
        self._primary_keys = {}
        self.update(arg, **kwargs)
    def __setitem__(self, key, value):
        super(MultipleKeyDict, self).__setitem__(key, value)
        self._primary_keys.setdefault(value, key)
    def __delitem__(self, key):
        value = self[key]
        super(MultipleKeyDict, self).__delitem__(key)
        if self._primary_keys[value] == key:
            del self._primary_keys[value]
            for k, v in super(MultipleKeyDict, self).iteritems():
                if v == value:
                    self._primary_keys[value] = k
                    break
    def __iter__(self):
        return self.iterkeys()
    def update(self, arg=None, **kwargs):
        if arg is not None:
            if isinstance(arg, collections.Mapping):
                for k in arg:
                    self[k] = arg[k]
            else:
                for k, v in arg:
                    self[k] = v
        for k in kwargs:
            self[k] = kwargs[k]
    def clear(self):
        super(MultipleKeyDict, self).clear()
        self._primary_keys.clear()
    def iteritems(self):
        for v, k in self._primary_keys.iteritems():
            yield k, v
    def items(self):
        return list(self.iteritems())
    def itervalues(self):
        return self._primary_keys.iterkeys()
    def values(self):
        return self._primary_keys.keys()
    def iterkeys(self):
        return self._primary_keys.itervalues()
    def keys(self):
        return self._primary_keys.values()

The only messy bit is that it has to search the whole dict in case a primary key gets deleted.

I omitted copy(), pop(), popitem() and setdefault(). If you need them, you'll have to implement them yourself.