You can always use the WithParameter
method to explicitly specify a constructor parameter:
builder.RegisterType<DoesSomething>()
.As<IDoesSomething>()
.WithParameter("helper", new HelperClass("do", "something"));
builder.RegisterType<DoesSomethingElse>()
.As<IDoesSomethingElse>()
.WithParameter("helper", new HelperClass("do", "somethingelse"));
As far as I can tell there is no need for an interface for HelperClass
because it essentially is just a value holder.
For this to work you would need to make the internal constructor public, I think.