Die errors and die varieties are different from one another. Die errors are like die cracks, broken dies, etc. There are too many of them to list, and they change with die usage. Nobody lists them, and most people don't care about them. Die varieties are doubled dies, repunched mintmarks, and over mintmarks. They are listable by die, and there are a number of different resources for them.
Die errors are very common, so a die error on a 1941S cent would be something many people have seen. An S/S would be a die variety, not a die error, and it would be a repunched mintmark, not a doubled die. The two terms are for completely different things. Doubled dies have nothing to do with the mintmark until after 1989, and repunched mintmarks only have to do with the mintmark and go up to 1989. The date has to do with a change in how dies were made. So, there is no such thing as "more than an S/S but not enough for a doubled die" - numismatically that statement makes no sense.
You probably have
Machine Doubling if the doubling you see affects more than the mintmark.
Machine Doubling is caused by a loose die in the striking chamber. It is very common and is neither a die error nor a die variety. It's not worth a premium value.