No, you can't; if you try this, you will get a ConcurrentModificationException when you use the iterator after modifying the map. The API documentation of class HashMap tells you:
The iterators returned by all of this class's "collection view methods" are fail-fast: if the map is structurally modified at any time after the iterator is created, in any way except through the iterator's own remove method, the iterator will throw a ConcurrentModificationException.
You cannot get a ListIterator for a HashMap, because ListIterator is for lists, and a map is not a list.
Find a different strategy for solving the problem; for example, first collect all the elements that you want to add to the map in a different map, and then when you're done iterating, use putAll() on the original HashMap to put the new elements in the map.