Is It Always Permissible to Add Another Independent Premise to an Argument

Is it always permissible to add another independent premise to an argument?

A) Yes, because no argument is ever truly complete.
B) Yes, because each independent premise begins a brand new line of argument.
C) Yes, because logic requires that every possible independent premise be included.
D) No, because if the argument is already complete, a new independent premise will add nothing.
E) No, because only new dependent premises may be added.