Yes, the 4516 did go on to a "4516-3", I have one.
However, the 4506 and 4516 were not stamped as such. There were stamped 4506-1's and 4516-2's. No 4506's stamped as -2, or -3, and no 4516's stamped as -3. Rather there were revisions, revision 3 and revision 4. The revisions consisted of engineering improvements, such as the barrel tab, slide mods ect.
IMHO, the "best" or most "desireable" of the 4506's is the 4506-3, or revision 4. It has laser etched markings, and is simply etched "4506" above the trigger guard. The ones I've shot have had uniformly great triggers, and were very accurate. There is no such thing, IMHO, as an undesireable 4506, so I'm biased
Hope this helps! Regards 18DAI.