I have never been all that interested in building a type set for my ancients. What i most appreciate is a good looking coin. Of course I would like to have at least one coin of every important historical leader or ruler, but I have no desire to acquire a heavily worn or corroded piece of some obscure ruler or one of a very short reign unless it was also a good looking coin. I have one decent Caligula but many of Augustus, Nero, Vespasian, Hadrian , that sort of coin. When I did actively collect US material I admit I did build up a type collection for a period of history. For example, for the administration of Jefferson I would have one example of each denomination in circulation when he was in office, except for the US gold of the period. For the Jacksonian Period I was able to add quarter and half eagles of the Classic Liberty set, and some nice broken bank notes. For the Civil War era, a few of the gold denominations and the odd ball two and three cent pieces, a few US fractional currencies and a blizzard of Confederate paper. But I did this for my US History students so they could see a progression of coinage and currency in the economic and financial changes in the course of US History. Their aesthetic appeal was not of much concern for my purposes, as they were and have remained for my ancient coins. A VG Liberty Seated half dollar was as good as an AU one for me. I don't think any of my ancients are less than a VF. I glance at my US coins, I gaze at my ancients.
I think it should be possible, as long as you exclude gold; I don't know about their sestertii but as far as silver goes, there should only be one type that is considerably rarer than the others.
I should have been more specific : that was meant pricewise I couldn't dream of a better home for that rare coin of the better style. When I first bought it some years ago you helped me at its precise ID : https://www.forumancientcoins.com/gallery/displayimage.php?pos=-38759 Q
I have mostly one coin for each emperor from Julius Caesar to Constantine the Great. I still have some holes that will never be filled such as Gordon Africanus I and II. Their coins cost a fortune, and they didn’t do that much. I have looked into the later emperors, but I don’t know that I am going to go there. Oddly enough, I still don’t have a Constantius. Every time I order a nice looking follis from a website, it’s been sold. I don’t need one from the short time he was emperor; one from his time as Caesar will do just fine. I have avoided biting the bullet and paying an expense silver coin. I could have done that long ago, but I really want to avoid doing that. I sprung for the Diocletian and Maximinus silver pieces, with the four leaders at the altar, but not for the caesars. I have had fun with this collection. I have built a historical “bullet point” notebook as I did with my British kings. I don’t want or need every type. That would impossible. I did collect a complete U.S. type set from the half cent to the “old gold” commemoratives as defined by the NGC registry. It took me over 50 years, but I finally did it.