Generally speaking, wives are equals. Both are equally married to the one husband. Any inequality is going to simply cause tension that could destroy the family.
However, this differs between cultures. In scripture we see for instance that Abraham's first wife Sarah was in authority over his second wife Hagar - she was a lower-status wife, a concubine. But that didn't exactly work out well, which shows the danger in such an arrangement. So it's possible - but not recommended. Also, you'd have an even harder time finding a second wife who was willing to actually marry you in those circumstances!
Scripture just says you must not reduce the conditions of the first wife when taking a second. In practice that's going to mean the first wife can't be put under the authority of the second, but it doesn't rule out the second being subject to the first.
It's worth pointing out that although scripture does not give any rule that wives must be equal, other religions add laws to that effect. The Quran for instance mandates that Muslim men must treat their wives completely equally. We are not bound to that in any way - but it serves to illustrate that others recognise a practical need for fair and equal treatment of wives, and shows the arrangement that has worked practically for centuries for untold thousands of Islamic families. It's good, time-tested advice, even though not mandatory for us.